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If hata and hatb are two unit vectors, t...

If `hata` and `hatb` are two unit vectors, then the vector `(hata + hatb) xx (hata xx hatb)` is parallel to

A

`(hat(a)-hat(b))`

B

`(hat(a)+hat(b))`

C

`(2hat(a)-hat(b))`

D

`(2hat(a)+hat(b))`

Text Solution

Verified by Experts

The correct Answer is:
A
`(hat(a)+hat(b))xx(hat(a)xxhat(b))`
`=hat(a)xx(hat(a)xxhat(b))+hat(b)xx(hat(a)xxhat(b))`
`=(hat(i).hat(b))hat(a)-(hat(a).hat(a)) hat(b)+(hat(b).hat(b))hat(a)-(hat(b).hat(a))hat(b)`
`=lambda hat(a)-hat(b)+hat(a)-lambda(b)`
`=lambda(hat(a)-hat(b))+1(hat(a)-hat(b))`.
`=(lambda+1)(hat(a)-hat(b))`
So, it is parallel to `hat(a)-hat(b)`.
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