If `vec A=hati +7hatj +hatk and vec B =2 hati+3hatj +4hatk` then the component of `vec A` along `vec B` is

Options

A. `(20)/(sqrt(23))`
B. `(27)/(sqrt(29))`
C. `(sqrt(29))/(27)`
D. `(22)/(sqrt(23))`

Answer

B

Explanation

The component of Along B is given by
`(vec A cdot vec B)/(|vec B|)=(A_(x)B_(x)+A_(y) B_(y) + A_(z)B_(z))/(sqrt(B_(x)^(2)+B_(y)^(2)+B_(z)^(2))`
`=((1xx2+7xx3+1xx4))/(sqrt(2^(2)+3^(2)+4^(2))`
`=(2+21+4)/(sqrt(4+9+16))=(27)/(sqrt(29))`