If `theta` is the angle between the vectors `a=2hati+2hatj-hatk and b=6hati-3hatj+2hatk`, then

Options

A. `costheta=(4)/(21)`
B. `costheta=(3)/(19)`
C. `costheta=(2)/(19)`
D. `costheta=(5)/(21)`

Answer

A

Explanation

Given, `a=2hati+2hatj-hatk` and
`b=6hati-3hatj+2hatk`
also, `theta` be the angle between them.
`thereforecostheta=(a*b)/(|a||b|)`
`=((2hati+2hatj-hatk)*(6hati-3hatj+2hatk))/(sqrt(4+4+1)sqrt(36+9+4))`
`=(12-6-2)/(3*7)=(4)/(21)`.