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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) (-3hat(i) +9hat(j) +5hat(k))`

B

`-3hat(i) +9hat(j) +5hat(k)`

C

`3hat(i)- 9hat(j) - 5hat(k)`

D

`(1)/(2) (3hat(i) +9hat(j) +5hat(k))`

Text Solution

Verified by Experts

The correct Answer is:
A
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