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If for two vectors vec(A) and vec(B), su...

If for two vectors `vec(A)` and `vec(B)`, sum `(vec(A)+vec(B))` is perpendicular to the difference `(vec(A)-vec(B))`. Find the ratio of their magnitude.

A

`1`

B

`2`

C

`3`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
`(vec(A) + vec(B)). (vec(A) - vec(B)) = 0`
`vec(A) . vec(A) - vec(A) . vec(B) + vec(B) . vec(A) - vec(B) . vec(B) = 0`
`A^(2) - B^(2) = 0 rArr A = B`
`(A)/(B) = 1`
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