Find the angle between the vectors `2hati-hatj+hatkand3hati+4hatj-hatk`.

Options

A. `theta=cos^(-1)((1)/(2sqrt39))`
B. `theta=cos^(-1)((1)/(sqrt39))`
C. `theta=cos^(-1)((1)/(2sqrt3))`
D. `theta=cos^(-1)((1)/(2sqrt7))`

Answer

A

Explanation

Let `veca=2veci-hatj+hatkandvecb=3hati+4hatj-hatk`
We know that, angle between two vectors `vecaandvecb` is given by
`costheta=(veca.vecb)/(|veca||vecb|)`
`=((2hati-hatj+hatk)(3hati+4hatj-hatk))/(sqrt4+1+1sqrt(9+16+1))`
`=(6-4-1)/(sqrt6sqrt26)=(1)/(2sqrt39)`
`:.theta=cos^(-1)((1)/(2sqrt39))`