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Let hat(alpha) = 3 hat(i)+hat(j) and h...

Let ` hat(alpha) = 3 hat(i)+hat(j)` and `hat(beta)= 2 hat(i)-hat(j)+3hat(k)`. If `vec(beta)=vec(beta)_(1)-vec(beta)_(2)`, where `vec(beta)_(1)` is parallel to `vec(alpha)` and `vec(beta)_(2)` is perpendicular to `vec(alpha)` then `vec(beta)_(1)xx vec(beta)_(2)` is equal to :

A

`(1)/(2)(3hati-9hatj+8hatk)`

B

`(1)/(2)(hati-3hatj+4hatk)`

C

`(1)/(2)(-3hati+9hatj+10hatk)`

D

`(3)/(2)(3hati+9hatj+10hatk)`

Text Solution

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The correct Answer is:
C
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