Two vectors, r and c, are equal: r = c. which of the following statements are true? (select all that apply.)
(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
(d) the directions of r and c may be different
(e) the magnitudes of r and c may be different
(f) the unit vector r must be equal to the unit vector c.

(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,

and

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

(1) , , and .

(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.