If the scalar product of the vector `hati+hatj+2hatk` with the unti vector along `mhati+2hatj+3hatk` is equal to 2, then one of the value of m is

Options

A. 3
B. 4
C. 5
D. 6

Answer

D

Explanation

`(hati +hatj +2 hatk ). ((mhati +2hatj +3hatk )/( sqrt(m^(2)+2^(2)+3^(2))))=2`
`implies m+2+6=2sqrt(13+m^(2))`
`implies (m+8)^(2)=4(13+m^(2))`
`implies m^(2)+16m+64 =4m^(2)+52`
` implies 3m^(2)-16m - 12=0 `
`implies (3m+2)(m-6)=0`
`implies m=6,-(2)/(3)`