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If |vecA + vecB| = |vecA - vecB|, then t...

If `|vecA + vecB| = |vecA - vecB|`, then the angle between `vecA and vecB` will be

A

`30^(@)`

B

`45^(@)`

C

`(60)^(@)`

D

`90^(@)`

Text Solution

Verified by Experts

The correct Answer is:
D
Let `theta` be angle between the vectors `vecA and vecB`, Then
`|vecA + vecB| = sqrt(A^(2) + B^(2) + 2AB cos theta)`
`|vecA - vecB| = sqrt(A^(2) + B^(2) - 2AB cos theta)`
According to given problem
`|veA + vecB| = |vecA - vecB|`
`therefore sqrt(A^(2) + B^(2) + 2AB cos theta) = sqrt(A^(2) + B^(2) - 2AB cos theta)`
Squaring both sides, we get
`A^(2) + B^(2) + 2AB cos theta = A^(2) + B^(2) - 2AB cos theta`
`therefore 4AB cos theta = 0`
As `A ne 0 , B ne 0 therefore cos theta = 0 or theta = 90^(@)`
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