If `vec(A)=2hat(i)+3hat(j)-hat(k)` and `vec(B)=-hat(i)+3hat(j)+4hat(k)`, then find the projection of `vec(A)` on `vec(B)`.

Options

A. `+ (1)/(sqrt3) (hat(i)- hat(j)- hat(k))`
B. `- (1)/(sqrt3) (hat(i) - hat(j)- hat(k))`
C. Both (a) and (b)
D. None of these

Answer

D

Explanation

`vec(C)= vec(A) xx vec(B)= |(hat(i),hat(j),hat(k)),(2,3,-1),(-1,3,4)|= 15 hat(i) - 7hat(j) + 9 hat(k)`
Unit vector perpendicular to both `vec(A) and vec(B)`
`hat(C)= (vec(C))/(|vec(C)|)= (15 hat(i) - 7hat(j) + 9 hat(k))/(sqrt(15^(2)+ (-7)^(2) + (9)^(2)))= (1)/(sqrt355) (15 hat(i)- 7hat(j) + 9hat(k))`