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If vec(v)(1)+vec(v)(2) is perpendicular ...

If `vec(v)_(1)+vec(v)_(2)` is perpendicular to `vec(v)_(1)-vec(v)_(2)`, then

A

`vec(v)_(1)` is perpendicular to `vec(v)_(2)`.

B

`|vec(v)_(1)|=|vec(v)_(2)|`

C

`vec(v)_(1)` is a null vector

D

The angle between `vec(v)_(1)` and `vec(v)_(2)` can have any value

Text Solution

Verified by Experts

The correct Answer is:
B, D
If two vectors are normal to each other, then their dot product is zero.
`(vec(v)_(1)+vec(v)_(2)).(vec(v)_(1)-vec(v)_(2))=0 rArrv_(1)^(2)-v_(2)^(2)=0`
`rArr v_(1)^(2)-v_(2)^(2)rArr v_(1)=v_(2)` or `|vec(v)_(1)|=|vec(v)_(2)|`
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