First slide

Vectors

Question

The sum of two vectors A and B is at right. angles to their difference. Then, the correct relation is

Moderate

A

A=B
B

A=2B
C

B = 2A
D

None of these

Solution

R·S = (A+ B)·(A $-$ B)
= A·A $-$ A·B+B ·A $-$ B·B
or 0 = A² $-$ B² ( $∵$ A·B = B·A)
$∴ A^{2} = B^{2} or A = B$

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