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Dahasolnce [82]
3 years ago
12

Two vectors, r and c, are equal: r = c. Which of the following statements are true? (Select all that apply.)

Physics
1 answer:
s344n2d4d5 [400]3 years ago
6 0

Answer:

(A) The y-component of r must be equal to the y-component of c

(B) The x-component of r must be equal to the x-component of c

(C) The z-component of r must be equal to the z-component of c

(F) The unit vector r must be equal to the unit vector c.

Explanation:

If two vectors are equal there are some conditions must be satisfy for the two vectors to be equal.

Let us suppose 2 vectors as,

A=a_{1}i+ a_{2}j+a_{3}k and

B=b_{1}i+ b_{2}j+b_{3}k

The conditions for the above two vectors should be equal are:

(1) a_{1}=b_{1}, a_{2}=b_{2}, and a_{3}=b_{3}.

(2) Unit vector of A must be equal to unit vector of B.

(3) Magnitude of both the vectors should be equal.

Now, according to question and observing above conditions of equality for r and c to be equal, the statements should be true are:

(A) The y-component of r should be equal to the y-component of c

(B) The x-component of r should be equal to the x-component of c

(C) The z-component of r should be equal to the z-component of c

(F) The unit vector r should be equal to the unit vector c.

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Answer:

\vec{F}_{21}=-5.63\times 10^{-11}N\\\\\vec{F}_{21}=\\

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F_{12}=\frac{kQ_1Q_2}{r^2}\\\\F_{12}= \frac{(9\times 10^9)(6)(1.602\times 10^{-19})^2}{(4.96\times 10^{-9})^2}\\\\F_{12}=5.63\times 10^{-11}N

Angle at which force F12 is acting is

\theta=tan^{-1}\frac{3.2}{3.8}\\\\\theta=tan^{-1}\frac{y}{x}\\\\\theta= 40.1^o

F_{x}=F_{12}cos\theta\\\\F_{x}=(5.63\times 10^{-11})cos(40.1)\\\\F_{x}=4.306\times 10^{-11}N\\\\F_{y}=F_{12}sin\theta\\\\F_{y}=(5.63\times 10^{-11})sin(40.1)\\\\F_{y}=3.62\times 10^{-11}N\\\\

\vec{F}_{12}=\vec{F}_{x}+\vec{F}_y\\\\\vec{F}_{12}=4.30\times 10^{-11}\,\hat{i} + 3.62\times 10^{-11}\,\hat{j}\\\\\vec{F}_{12}=

Force exerted on charge -2e is equal in magnitude to F12 but is in opposite direction

F_{21}=-5.63\times 10^{-11}N

\vec{F}_{21}=

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