Question

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

Answer 1

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.