Question

Write a vector of magnitude of 18 units in the direction of the vector `hati - 2hatj - 2hatk`.

Answer 1

Let `veca = hati - 2hatj - 2hatk`

Then, `|veca| = sqrt(1^2 + (-2)^2 + (-2)^2`

= `sqrt(1 + 4 + 4)`

= `sqrt(9)`

= 3

∴ Unit vector, `hata = veca/|veca|`

= `1/3 hati - 2/3hatj - 2/3hatk`

Hence, the required vector of magnitude 18 units is `18hata`.

∴ Required vector = `18/3 hati - 36/3 hatj - 36/3 hatk`

= `6hati - 12hatj - 12hatk`