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Two vectors vec(A) and vec(B) are such t...

Two vectors `vec(A)` and `vec(B)` are such that `|vec(A)+vec(B)|=|vec(A)-vec(B)|` then what is the angle between `vec(A)`and `vec(B)` :-

A

`0^(@)`

B

`90^(@)`

C

`60^(@)`

D

`120^(@)`

Text Solution

Verified by Experts

The correct Answer is:
B
`|vec A+vec B|=|vec A - vec B|`
`therefore |vec A + vec B|^(2)= |vec A - vec B|^(2)`
`|vec A + vec B| cdot |vec A + vec B|=|vec A-vec B| cdot |vec A - vec B|`
`therefore vec A cdot vec A + vec A cdot vec B+vec B cdot vec A+vec B cdot vec B`
`=vec A cdot vec A - vec A cdot vec B - vec B cdot vec A + vec B cdot vec B`
`=vec A cdot vec A - vec A cdot vec B cdot vec A + vec B cdot vec B`
`therefore A^(2) +2vec A cdot vec B + B^(2) =A^(2) -2vec A cdot vec B + B^(2)`
`therefore 2vec A cdot vec B =- 2vec A cdot vec B`
`therefore 4 vec A cdot vec B =0" "therefore vec A cdot vec B =0`
`therefore vec A bot vec B" or "theta =90^(@)`
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