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If veca is any vector, then (vec a xx ...

If `veca` is any vector, then `(vec a xx vec i)^2+(vec a xx vecj)^2+(veca xx vec k)^2` is equal to

A

`a^(2)`

B

`2a^(2)`

C

`3a^(2)`

D

`0`

Text Solution

Verified by Experts

The correct Answer is:
B
Let `a=a_(1)hati+a_(2)hatj+a_(3)hatk`
`therefore(axxhati)^(2)+(axxhatj)^(2)+(axxhatk)^(2)`
`=(a_(3)^(2)+a_(2)^(2))+(a_(1)^(2)+a_(3)^(2))+(a_(2)^(2)+a_(1)^(2))`
`=2(a_(1)^(2)+a_(2)^(2)+a_(3)^(2))=2a^(2)`
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