Vectors A and B have equal magnitudes. Which statement is always true? Justify it!

a. A + B = 0.

b. A - B = 0.

c. A - B is perpendicular to A + B.

d. B - A is perpendicular to A - B.

e. The magnitude of A - B equals the magnitude of A + B

c) A - B is perpendicular to A + B

Explanation:

a) and b) is not true when A and B are inclined at some angle.

d) is wrong because A - B can not be perpendicular to B - A when they are linear because each will be equal to zero.

e) is wrong because magnitude of A + B will be more than magnitude of

A - B when angle between them is acute.

So c) option is right.

(A + B) dot product (A - B) = A² - B² = 0

Hence (A + B) is perpendicular to (A - B).