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vectors veca and vecb are inclined at an...

vectors `veca and vecb` are inclined at an angle ` theta = 60^(@). " If " |veca|=1, |vecb| =2 , " then " [ (veca + 3vecb) xx ( 3 veca -vecb)] ^(2)` is equal to

A

225

B

275

C

325

D

300

Text Solution

Verified by Experts

The correct Answer is:
D
we have,
` [ (veca + 3vecb) xx (3 veca -vecb)]^(2)`
` = [ 10 (vecb xx veca )]^(2)`
` = 100 |vecb xx veca|^(2)`
` 100 { |veca|^(2) |vecb|^(2) -(veca .vecb)^(2)}`
` 100 ( 4 -2 cos 60^(@)) = 300 , " " [ veca .vecb = 2 cos 60^(@) =1]`
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