Find the unit vector parallel to the resultant vector of `2hati+4hatj-5hatk and hati+2hatj+3hatk`.

Options

A. `(1)/(7)(3hati+hatj+hatk)`
B. `(hati+hatj+hatk)/(sqrt(3))`
C. `(hati+hatj+2hatk)/(sqrt(6))`
D. `(1)/(sqrt(69))(-hati-hatj+8hatk)`

Answer

A

Explanation

Resultant vector`=(2hati+4hatj-5hatk)+(hati+2hatj+3hatk)`
`=3hati+6hatj-2hatk`
Unit vector`=(3hati+6hatj-2hatk)/(sqrt(9+36+4))=(1)/(7)(3hati+6hatj-2hatk)`.