The unit vector normal to the plane containing `vec(a)=(hat(i)-hat(j)-hat(k)) and vec(b)=(hat(i)+hat(j)+hat(k)) ` is

Options

A. `(hat(j)-hat(k))`
B. `(-hat(j)+hat(k))`
C. `(1)/(sqrt(2))(-hat(j)+hat(k))`
D. `(1)/(sqrt(2))(-hat(i)+hat(k))`

Answer

C

Explanation

`(vec(a)xxvec(b))=|(hat(i),hat(j),hat(k)),(1,-1,-1),(1,1,1)|=(-2hat(j)+2hat(k))`
`rArr |vec(a)xxvec(b)|=sqrt((-2)^(2)+2^(2))=sqrt(8)=2sqrt(2)`
`rArr ` required vector`=(2(-hat(j)+hat(k)))/(2sqrt(2))=(1)/(sqrt(2))(-hat(j)+hat(k))`.