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Let vecalpha=3hati+hatj,vec(beta)=2hati-...

Let `vecalpha=3hati+hatj,vec(beta)=2hati-hatj` and `vec(beta)=vec(beta_(1))-vec(beta_(2))`, such that `vec(beta_(1))` is parallel to `vec(alpha)` and `vec(beta_(2))` is perpendicular to `vec(alpha)`. Find `vec(beta_(1))xxvec(beta_(2))`.

A

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

B

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

C

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

D

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

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The correct Answer is:
C
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