Question

Find `lambda` if the scalar projection of `vec a = lambda hat i + hat j + 4 hat k` on `vec b = 2hati + 6hatj + 3hatk` is 4 units

Answer 1

Projection of `vec a` on `vec b` is `(vec a . vec b)/|vecb| = 4`

`= ((lambdahati + hatj + 4hatk).(2hati+6hatj + 3hatk))/(sqrt(2^2 + 6^2 + 3^2)) = 4`

`:. (2lambda + 6(1) + 4(3))/sqrt49  = 4`

`:. (2lambda + 18)/7  = 4`

`:. 2lambda = 28 - 18 `

`:. 2lambda = 10`

`lambda = 5`