Question

Find a vector of magnitude 20 units parallel to the vector `2hati + 5hatj + 4hatk`.

Answer 1

Given vector, `veca = 2hati + 5hatj + 4hatk`

`|veca| = sqrt(2^2 + 5^2 + 4^2)`

= `sqrt(4 + 25 + 16)`

= `sqrt(45)`

= `3sqrt(5)`

∴ `hata = veca/|veca|`

= `(2hati + 5hatj + 4hatk)/(3sqrt(5)`

Thus, the vector of magnitude 20 units and parallel to the `veca` is:

= `± 20. hata`

= `± (20(2hati + 5hatj + 4hatk))/(3sqrt(5))`

= `± (40hati)/(3sqrt(5)) ± (100hatj)/(3sqrt(5)) ± (80hatk)/(3sqrt(5))`

= `± (8sqrt(5))/3hati ± (20sqrt(5))/3hatj ± (16sqrt(5))/3hatk`