If `vec(beta)` is perpendicular to both `vec(alpha) and vec(lambda)` where `vec(alpha)=hat(k) and vec(lambda)=2hat(i)+3 hat(j)+4 hat(k)`, then what is `vec(beta)` equal to ?

Options

A. `3hat(i)+2hat(j)`
B. `-3hat(i)+2hat(j)`
C. `2hat(i)-3hat(j)`
D. `-2hat(i)+3hat(j)`

Answer

B

Explanation

Let `vec(beta)=a hat(i)+b hat(j)+c hat(k)`
Since `vec(beta).vec( alpha)=0 and vec(beta).vec(lambda)=0`
`:. C=0 and 2a + 3b=0 rArr a = - (3b)/(2)`
Hence, `vec(beta)=-(3 b)/(2) vec(i)+b hat(j)=0 rArr -3 hat(i)+2 hat(j)=0`