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If vec(A)=2hat(i)+hat(j)+hat(k) and vec(...

If `vec(A)=2hat(i)+hat(j)+hat(k)` and `vec(B)=hat(i)+hat(j)+hat(k)` are two vectors, then the unit vector is

A

Perpendicular to `vec(A)` is `(-hat(j)+hat(k))1/sqrt(2)`

B

Parallel to `vec(A)` is `(2hat(i)+hat(j)+hat(k))/sqrt(6)`

C

Perpendicular to `vec(B)` is `((-hat(j)+hat(k))/sqrt(2))`

D

Parallel to `vec(A)` is `(hat(i)+hat(j)+hat(k))/sqrt(3)`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
`vec(A)xxvec(B)=|(hat(i), hat(j), hat(k)) ,(2,1,1), (1 ,1 ,1)|`
`hat(i)(1-1)-hat(j)(2-1)+hat(k)(2-1)=-hat(j)+hat(k)`
The unit vector perpendicular to `vec(A)` and `vec(B)` is `((-hat(j)+hat(k))/sqrt(2))`.So choice (a) and (c ) are correct.
Any vector whose magnitude is K (constant) times `(2hat(i)+hat(j)+hat(k))` is parallel to `vec(A)`.
So, unit vector `(2hat(i)+hat(j)+hat(k))/sqrt(6)` is parallel to `vec(A)`.
So, choice (b) is correct.
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