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 ) .

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