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if veca=3hati+2hatj+2hatk and vecb=hati+...

if `veca=3hati+2hatj+2hatk` and `vecb=hati+2hatj-2hatk` then a vector of magnitude 12, which is perpedicular to both `veca+vecb` and `veca-vecb` is

A

`4(2hati+2hatj+hatk)`

B

`4(2hati+2hatj-hatk)`

C

`4(-2hati-2hatj+hatk)`

D

`4(2hati-2hatj-hatk)`

Text Solution

Verified by Experts

The correct Answer is:
D
`(veca+vecb)xx(veca-vecb)=lambda|(hati,hatj,hatk),(4,4,0),(2,0,4)|=hati(16)-hatj(16)+k(-8)=lambda(2hati-2hatj-hatk)`
`|lambda(2hati-2hatj-k)||3lambda|=12" "rArr" "lambda=4" "therefore" "8hati-8hatj-4hatk` is required vector
i.e., `4(2hati-2hatj-hatk)`
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