Question

A vector `veca` of magnitude 14 has direction ratios <2, 3, −6>. Find the projection of the vector `veca  "on"  hati`.

Answer 1

Given direction ratios of `veca` (2, 3, −6),

Magnitude of direction ratios:

= `sqrt(2^2 + 3^2 + (-6)^2)`

= `sqrt(4 + 9 + 36)`

= `sqrt49`

= 7

Unit vector in the direction of `veca: (2hati + 3hatj - 6hatk)/7`

Since `|veca| = 14`,

`veca = 14((2hati + 3 hatj - 6hatk)/7)`

`veca = 2(2hati + 3 hatj - 6hatk)`

`veca = 4hati + 6 hatj - 12hatk`

Hence, the projection of the vector `veca  "on"  hati` is 4.