Question

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

Answer 1

c ) A - B is perpendicular to A + B

Step-by-step 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 ) .