Question

Find a vector of magnitude 5 units, and parallel to the resultant of the vectors `veca = 2i + 3hatj - hatk` and `vecb = hati - 2hatj + hatk`.

Answer 1

We have `veca = 2hati + 3hatj - hatk, vecb = hati - 2hatj + hatk`

Let be the resultant of c and a.

Then,

`vecc = veca + vecb = (2 + 1)hati + (3 - 2)hatj + (-1 + 1)hatk = 3hati + hatj`

`|vecc| = sqrt(3^2 + 1^2) = sqrt(9 + 1) = sqrt10`

`hatc = vecc/|vecc| = (3hati + hatj)/sqrt10`

Therefore, the resultant is a vector of five units that is parallel to the results of vectors a and b.

⇒ `±5.c = ±5 xx (1/sqrt10)(3hati + hatj) `

`= ±(3sqrt10hati)/2 ± sqrt10/2hatj`.