Given three points are `A(-3,-2,0),B(3,-3,1)a n dC(5,0,2)dot` Then find a vector having the same direction as that of ` vec A B` and magnitude equal to `| vec A C|dot`

Explanation

Given points are `A(-3, -2, 0), B(3, -3, 1) and C(5, 0, 2)`. Therefore,
`" "vec(AB)=6hati-hatj+hatk`
and `" "vec(AC)=8hati+2hatj+2hatk`
`" "|vec(AC)|=sqrt(64+4+4)=sqrt(72)`
Unit vector in direction of `vec(AB)` is `(6hati-hatj+hatk)/(sqrt(38))`
`therefore" "`Required vector
`" "=(sqrt(72))/(sqrt(38))(6hati-hatj+hatk)= (6)/(sqrt(19))(6hati-hatj+hatk)`