The unit vector parallel to the resultant of the vectors `2hati+3hatj-hatk` and `4hati-3hatj+2hatk` is

Options

A. `1/sqrt(37)(6hati+hatk)`
B. `1/sqrt(37)(6hati+hatj)`
C. `1/sqrt(37)(6hati+hatk)`
D. none of these

Answer

A

Explanation

Let `vecR` be the resultant of the given vectors.
Then, `vecR=(2hati+3hatj-hatk)+4(hati-3hatj+2hatk)`
`=6hati+0hatj+hatk`
The required unit vector parallel to `vecR`.
`vecR/|vecR|=(6hati+0hatj+hatk)/sqrt(6^(2)+0^(2)+1^(2)) = (6hati+0hatj+hatk)/sqrt(37)`
`=1/sqrt(37)(hati+hatk)`