Answers
Answer:
[tex]\vec{A} + \vec{B} = \vec{A} - \vec{B}[/tex] if and only if [tex]\vec{B}[/tex] is a zero vector.
Explanation:
An equation is true if and only if adding the same value to both sides of the equation (the value needs to be compatible) gives an equation that is also true.
Start with the [tex]\vec{A} + \vec{B} = \vec{A} - \vec{B}[/tex].
This equation is true if and only if [tex]\left(\vec{A} + \vec{B}\right) + \vec{B} = \left(\vec{A} - \vec{B}\right) + \vec{B}[/tex] ([tex]\vec{B}[/tex] is added to both sides of the original equation.)
Vector addition and subtraction are associative. Therefore, [tex]\left(\vec{A} + \vec{B}\right) + \vec{B} = \left(\vec{A} - \vec{B}\right) + \vec{B}[/tex] if and only if [tex]\vec{A} + \left(\vec{B} + \vec{B}\right) = \vec{A} + \left(- \vec{B} + \vec{B}\right)[/tex], which is equivalent to [tex]\vec{A} + 2\, \vec{B} = \vec{A}[/tex].
[tex]\vec{A} + 2\, \vec{B} = \vec{A}[/tex] if and only if [tex]\left(-\vec{A}\right) + \vec{A} + 2\, \vec{B} = \left(-\vec{A}\right) + \vec{A}[/tex] ([tex]\left(-\vec{A}\right)[/tex]is added to both sides of this equation,) which is equivalent to [tex]2\, \vec{B} = \vec{0}[/tex].
[tex]2\, \vec{B} = \vec{0}[/tex] if and only [tex]\displaystyle \frac{1}{2} \cdot \left(2\, \vec{B}\right) = \frac{1}{2} \cdot \vec{0}[/tex], which is equivalent to [tex]\vec{B} = \vec{0}[/tex]. That is: [tex]\vec{B}[/tex] is the zero vector.
In other words:
[tex]\begin{aligned}& \vec{A} + \vec{B} = \vec{A} - \vec{B}\\ &\iff \left( \vec{A} + \vec{B}\right) + \vec{B} = \left(\vec{A} - \vec{B}\right) + \vec{B} \\ &\iff \vec{A} + \left(\vec{B} + \vec{B}\right) = \vec{A} + \left(- \vec{B} + \vec{B}\right) \\ & \iff \vec{A} + 2\, \vec{B} = \vec{A} \\ & \iff \left(-\vec{A}\right) + \vec{A} + 2\, \vec{B} = \left(-\vec{A}\right) + \vec{A} \\ &\iff 2\, \vec{B} = \vec{0} \\ &\iff \frac{1}{2} \cdot 2\,\vec{B} = \frac{1}{2} \cdot \vec{0} \\ &\iff \vec{B} = \vec{0}\end{aligned}[/tex].
Hence, [tex]\vec{A} + \vec{B} = \vec{A} - \vec{B}[/tex] if and only if [tex]\vec{B}[/tex] is the zero vector.
Related Questions
Carbon dioxide can be represented by the chemical formula
es
A)
C₂0
B)
CO2
C)
Ca,
D)
CaOz
pls help fast !!!
Answers
Answer:
Your answer is B co2
Explanation:
Answer: CO2
Explanation:
Carbon dioxide is consisted of one carbon molecule and 2 oxygen molecules, therefore CO2
number of atoms of each element Sulfur dioxide?
Answers
Answer:
Element Symbol # of Atoms
Oxygen O 2
Sulfur S 1
Explanation:
A 230 kg motorcycle zooms away from a red light with a force of
13,800 Newtons. What is the acceleration of the motorcycle in m/s??
Answers
Answer:343
Explanation:
AP Physics Question 3
A planet has two moons, Moon and Moon , that orbit at different distances from the planet’s center, as shown.
Astronomers collect data regarding the planet, the two moons, and their obits. The astronomers are able to estimate
the planet’s radius and mass.
3. The masses of the two moons are determined to be for Moon and for Moon . It is observed that
the distance between Moon and the planet is two times that of the distance between Moon and the
planet. How does force exerted from the planet on Moon compare to the force exerted from the planet on
Moon ?
The gravitational force exerted from the planet on Moon is two times larger than the gravitational force
exerted from the planet on Moon .
B
The gravitational force exerted from the planet on Moon is eight times larger than the gravitational force
exerted from the planet on Moon .
C
The gravitational force exerted from the planet on Moon is two times smaller than the gravitational force
exerted from the planet on Moon .
D
The gravitational force exerted from the planet on Moon is eight times smaller than the gravitational force
exerted from the planet on Moon .
Answers
Gravitational force increases as the mass increases and decreases as the distance between the bodies is increased.
The correct option is; The gravitational force exerted from the planet on Moon A is eight times larger than the gravitational force exerted from the planet on Moon B.Reasons:
The given parameters are;
The moons of the planet = Moon A and Moon B
Mass of Moon A = 2·M
Mass of moon B = M
The distance between Moon B and the planet = 2 × The distance between Moon A and the planet
Required:
Comparison (compare) of the force exerted from the planet on Moon A and Moon B.
Solution:
The force, F, exerted from the planet is the gravitational force which is given by Newton's Law of Gravitation as follows;
[tex]\displaystyle F = \mathbf{G \cdot \frac{M_{planet} \times M}{R^2}}[/tex]Where;
G = Universal gravitational constant
[tex]M_{planet}[/tex] = Mass of the planet
M = Mass of the Moon
R = The distance from the planet to the Moon
For Moon A, we have;
Mass = 2·M
Distance = R
Which gives;
[tex]\displaystyle F_A = G \cdot \frac{M_{planet} \times 2\cdot M}{R^2} = 2\cdotG \cdot \frac{M_{planet} \times M}{R^2} = \mathbf{2 \cdot F}[/tex]
With Moon B, we have;
Mass = M
Distance = 2·R
Therefore;
[tex]\displaystyle F_B = G \cdot \frac{M_{planet} \times M}{(2 \cdot R)^2} = G \cdot \frac{M_{planet} \times M}{4 \cdot R^2} = \frac{1}{4} \cdot G \cdot \frac{M_{planet} \times M}{R^2} = \mathbf{\frac{1}{4} \cdot F}[/tex]
Which gives;
[tex]\displaystyle \frac{F_A}{F_B} = \frac{2 \cdot F}{\frac{1}{4} \cdot F } =2 \times \frac{4}{1} = \mathbf{8}[/tex]
[tex]\displaystyle \frac{F_A}{F_B} = 8[/tex]
[tex]F_A = \mathbf{8 \times F_B}[/tex]
The force from the planet on Moon A, [tex]F_A[/tex], is 8 times the force from the planet on Moon B.
Therefore, whereby option B is;
The gravitational force exerted from the planet on Moon A is eight times larger than the gravitational force exerted from the planet on Moon B.The correct option is option B
Learn more about Newton's Law of gravitation here:
https://brainly.com/question/18670622
Joey's little brother makes a ramp to push hos toy dump truck up to his sandbox. if he uses 5N of force to push the 12N truck up the ramp, what is the mechanical advantage of his ramp?
A. 6.0
B.0.42
C. 2.4
D. 23.5
Answers
Which team is defense?
Answers
Answer:
What are the teams? Football would be defense...
Explanation:
sorry if this didn't answer your question...
Answer:
The team without possession of the ball (B)
Explanation:
Suppose a small black hole with mass equal to 7.35 × 10^30 kg drifted past Earth at the same distance as the Moon. The mass of the Moon is about 7.35 × 10^22 kg. What might be expected? (Please do not answer if you do not know, this is for a project worth 30% of my grade)
Answers
Answer:
wt f i dont care
Explanation:
How many lobes are in the lungs
Answers
Answer:
There are 5 lobes in the lungs.
Explanation:
The right lung consists of three lobes: the RUL, the RML, and the RLL. While the left lung consists of two lobes: the LUL, and the LLL.
How are amplitude, intensity, and
loudness related?
Answers
Answer:
Amplitude is a measure of the size of sound waves. It depends on the amount of energy that started the waves. Greater amplitude waves have more energy and greater intensity, so they sound louder. The same amount of energy is spread over a greater area, so the intensity and loudness of the sound is less.
Explanation:
17) An object is being pulled in two different directions by two students. One student pulls to the left with 12 N
and the other pulls to the right with 15 N. What is the net force on the object?
a) 27 N right.
b) 3 N right
c) 2 N left.
d) 3 N left.

Answers
An oscillator is made with a rubber band and a block of wood
as shown in the diagram. What happens to the oscillator if we
make the block of wood heavier?
Answers
Answer:
Explanation:
a. The frequency increases.
b. The period increases.
c. The frequency stays the same.
d. The period stays the same
If you use a lever to lift a boulder 0.25m, while applying 350 N on the lever which moves 1.5 m down on your side. What is the weight of the boulder? (F1d1 = F2d2) 87.5 N 131 N 525 N 2100 N
Answers
Answer:
2100 N
Explanation:
From the question,
Using the formula
F₁d₁ = F₂d₂..................... Equation 1
Where F₁ = Weight of the Boulder, d₁ = distance moved by the Boulder, F₂ = Force applied on the lever, d₂ = distance moved by the lever.
make F₁ the subject of the equation
F₁ = F₂d₂/d₁.................... Equation 2
Given: F₂ = 350 N, d₁ = 0.25 m, d₂ = 1.5 m
Substitute these values into equation 2
F₁ = 350(1.5)/0.25
F₁ = 2100 N
What is the wavelength of visible light emitted at 4.2 x 10^8 Answer in units of M
Answers
Answer:
0.714 m
Explanation:
From the question,
v = λf......................... Equation 1
Where v = velocity of visible light, f = frequency of visible light, λ = wave length of visible light.
make λ the subject of the equation
λ = v/f.................. Equation 2
Given: f = 4.2×10⁸ Hz
Note: Light is an electromagnetic wave, and all electromagnetic waves travels with the same speed (3×10⁸ m/s)
Constant: v = 3×10⁸ m/s
Substitute these values into equation 2
λ = 3×10⁸/4.2×10⁸
λ = 0.714 m
Which statement describes this image
Answers
Answer:
3rd one i think.
Explanation:
Which three parts of the graph’s curve represent the solid, liquid, and gaseous state of water? Explain your reasoning.
Answers
B,C,D maybe
Explanation:
plz dont get mad
Which of the following did you include in your response? Check all that apply. Absolute strength measures maximum force. Dynamic strength measures repeated motions Elastic strength measures exertion of force rapidly Strength endurance measures fatigue resistance
Answers
Answer:
d
Explanation:
Answer:
any answer would be correct. its a choose your own answer question lol
Explanation:
This girl named Emma she my crush what do I say to her.
Answers
Answer:
you gotta shoot your shot.
Explanation:
look for the signs. ask her out before someone else does. you got this dawg
A car slams into a wall with a force of 5000 N. What is the force of the wall on the car? 5000 N -5000 N 49000 N 510 N It cannot be determined with the information provided.
Answers
Answer:
-5000 N
Explanation:
Newtons third law of motion states that action and reaction are equal and opposite. This means that to every action, there is an equal opposite reaction.
Hence when a body A exerts a force FA on another body B, the body B also exerts a force FB on A which is equal in magnitude to FA but opposite in direction. FB is the reaction force due to FA.
Hence, when a car hits a wall with a force of 5000N, the reaction of the wall on the car is -5000N
I was playing goalie in a soccer league and made a save. The ball was traveling at 14 m/s and has a mass of 0.45 kg. How muck kinetic energy did the ball have when it hit me
Answers
Answer:
Kinetic energy = 44.1 J
Explanation:
Given:
Velocity of ball = 14 m/s
Mass of ball = 0.45 kg
Find:
Kinetic energy
Computation:
An item's kinetic energy is force it has as a result of its motion. It is the amount of work necessary to move a body of a known volume from rest to a specified velocity.
Ke = (1/2)(m)(v²)
Ke = (1/2)(0.45)(14²)
Ke = (1/2)(0.45)(196)
Kinetic energy = 44.1 J
A force of 40 N stretches a spring 0.20 m what is the spring
constant?
a. 2000 N/m
b. 200 N/m
c. 20 N/m
d. 2 N/m
Answers
1.) True or False.
The two forces in an action-reaction pair are always equal in strength.
2.) True or False.
The two forces in an action-reaction pair act in the same direction.
3.) True or False.
Action-reaction force pairs act on the same object.
4.) True or False.
Action-reaction force pairs act simultaneously.
Answers
Answer:
Explanation:
According to Newton's third law of motion, forces always act in equal but opposite pairs. Another way of saying this is for every action, there is an equal but opposite reaction. This means that when you push on a wall, the wall pushes back on you with a force equal in strength to the force you exerted. 1.True 2.falues 3.true 4. not really sure on this one
what is 1 AU equal to in kilometres
Answers
Answer:
1 au is 1.496e+8 kilometres
Explanation:
Easy AU to km conversion. A kilometer, or kilometre, is a unit of length equal to 1,000 meters, or about 0.621 miles.
Hope this helps :)
what is SI unit of speed
Answers
Answer:
m/s
Explanation:
The SI unit of speed is the metre per second, but the most common unit of speed in everyday usage is the kilometre per hour or, in the US and the UK, miles per hour.
m/s
which is also written as
ms-¹
The above mentioned symbols are said as 'meter per second'
hope it helps!
Two charges of 5 x 10-6 C are a certain distance apart. These two positive charges experience 3.6 N of repelling electrical force between them. How far apart are these charges?
Answers
Answer:
r = 0.2499 m
Explanation:
Use Coulomb's Law: [tex]F_{e} = kq_{1}q_{2} / r^{2}[/tex] where Fe is the electric force, q1 and q2 are the 2 charges respectively, k is a constant (8.99*10^9 N • m^2 / C^2) and r is the distance.
[tex]3.6 N = (8.99*10^{9})(5*10^{-6})(5*10^{-6}) / r^{2}[/tex]
r = 0.2499 m
The distance that should be apart from these charges should be considered when the r = 0.2499 m.
Calculation of the distance apart:Since
Two charges of 5 x 10-6 C are a certain distance apart. These two positive charges experience 3.6 N of repelling electrical force between them
So
here we use Columb law
Electric force = k * two charges * two charges)r^2
3.6 N = (8.99*10^9) * ( 5 * 10^-6) * (5*10^-6)r^2
r = 0.2499 m.
Hence, The distance that should be apart from these charges should be considered when the r = 0.2499 m.
Learn more about force here: https://brainly.com/question/15866225
Please hurry
Starting from rest, this airliner accelerates at 2.4m/s2 for 32 seconds before leaving the ground. Calculate its velocity at liftoff.
Answers
Answer:
The velocity will be "76.8 m/s".
Explanation:
The given values are:
Acceleration,
a = 2.4 m/s²
Time,
t = 32 seconds
By equation of motion,
⇒ [tex]v=u+at[/tex]
On substituting the values, we get
⇒ [tex]=0+2.4\times 32[/tex]
⇒ [tex]=0+76.8[/tex]
⇒ [tex]=76.8 \ m/s[/tex]
Keegan has a wood ball, James has a steel ball, and Drew has a ping pong ball. If they all blow them with the same air force across a table using a straw, whose ball with will win the race?
Answers
Answer:
A ping pong ball
Explanation:
It has the lightest weight among the rest
How much energy (in kWh) can you get from a 72 cell solar panel in one year?
Answers
Explanation:
Question 13 of 20
A copper atom has an atomic number of 29 and an atomic mass of 64. What
is the structure of this atom?
A. It has a central nucleus composed of 29 protons and 29 neutrons,
surrounded by an electron cloud containing 35 electrons.
B. It has a central nucleus composed of 29 protons and 35 neutrons,
surrounded by an electron cloud containing 29 electrons.
O C. It has a central nucleus composed of 35 protons and 29 neutrons,
surrounded by an electron cloud containing 29 electrons.
D. It has a central nucleus composed of 29 protons and 64 neutrons,
surrounded by an electron cloud containing 29 electrons.
SUBMIT
Answers
Answer:
B. It has a central nucleus composed of 29 protons and 35 neutrons,
surrounded by an electron cloud containing 29 electrons.
Explanation:
Protons and neutrons are the only subatomic particles with mass, and they are located in the nucleus. If this atom has an atomic number of 29 and is copper, it must have 29 protons (protons define which element is being observed). This means all remaining mass is from neutrons. 64-29 = 35.
Electrons have no mass and orbit the nucleus in the electron cloud. Since this copper atom is neutral (we are not told it has a charge), there must be an equal number of protons and electrons.
Answer:
B. It has a central nucleus composed of 29 protons and 35 neutrons,
surrounded by an electron cloud containing 29 electrons.
Explanation:
Hope this helps
When melting of a metamorphic rock occurs, it changes into what?
Answers
Answer:
The upper limit of metamorphism occurs at the pressure and temperature of wet partial melting of the rock in question. Once melting begins, the process changes to an igneous process rather than a metamorphic process. During metamorphism the protolith undergoes changes in texture of the rock and the mineral make up of the rock.
Explanation:
i hope this helps
When melting of a metamorphic rock occurs, it changes into Magma and igneous rock will emerge as a result of this..
What is metamorphism?Sedimentary, igneous, and metamorphic rocks are the three distinct types of rocks that make up the rock cycle. Rocks such as sedimentary and igneous rocks were not always rocks.
A very particular set of circumstances must exist for a rock to undergo metamorphism. It is necessary to subject the preexisting rock to extreme temperatures, high pressures, or hot, mineral-rich fluids. All three of these conditions are typically true. The Earth's crust is where these conditions are most frequently encountered, either there or at plate borders when tectonic plates meet.
It is essential that the current rock not melt in order to produce metamorphic rock. The rock will melt under excessive heat or pressure and turn into magma. Instead of a metamorphic rock, an igneous rock will emerge as a result of this.
Learn more about metamorphism here:
https://brainly.com/question/1100440
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whar determines the direction of ocean currents
Answers
Answer:
The direction in which they rotate is determined by the hemisphere in which they are located. The main overall global wind patterns, the rotation of the Earth, and the shape of ocean basins are the three major factors that decide surface currents.
Oceanic factors are Tempature, salinity, density, pressure gradient and melting of ice. Atsmopheric factors are atsmopheric pressure, winds, rainfall, evaporation and insolation