If `a=hati-hatj-hatk and b= lambda hati-3hatj+ hatk` and the orthogonal projection of b on a is `(4)/(3) (hati-hatj-hatk)` then `lambda` is equal to

Options

A. 0
B. 2
C. 12
D. `-1`

Answer

B

Explanation

Given `((hatb*hata)hata)/(|hata|^(2))=(4)/(3)(hati-hatj-hatk)`
`rArr ({(lambda hati-3)+hatk(hati-hatj=-hatk)}(hati-hatj-hatk))/((1+1+1))`
`=(4)/(3) (hati-hatj-hatk)`
`rArr (lambda+3-1) (hati-hatj-hatk)= 4(hati-hatj-hatk)`
`rArr (lambda+2)(hati-hatj-hatk)=4(hati-hatj-hatk)`
On equqtionn the coefficient of `hati`, we get
`lambda+2=4 rArr lambda=2`