Question

A person standing at O(0, 0, 0) is watching an aeroplane which is at the coordinate point A(4, 0, 3). At the same time, he saw a bird at the coordinate point B(0, 0, 1). Find the angles which `overset->(BA)` makes with the x, y and z axes.

Answer 1

`overset->(OA) = 4hati + 3hatk`

`overset->(OB) = hatk`

`overset->(BA) = overset->(OA) - overset->(OB)`

= `(4hati + 3hatk) - hatk`

= `4hati + 2hatk`

`|overset->(BA)| = sqrt(16 + 4)`

= `sqrt20`

= `2sqrt5`

`hat(BA) = 4/(2sqrt5)hati +2/(2sqrt5)hatk`

= `2/sqrt5hati + 1/sqrt5hatk`

So, the angles made by the vector `overset->(BA)` with the x, y and the z axes are respectively `cos^-1(2/sqrt5), pi/2, cos^-1(1/sqrt5)`.