A vector n of magnitude 8 units is inclined to the x-axis is 45o, y-axis at 60o and an acute angle with the z-axis. If a plane passes through a point (2,−1,1) and is normal to n, find its equation in vector form.
If α,β, and γ are the angles made by the line segment with the coordinate axis.
cosα,cosβ and cosγ are called as the direction cosines and are usually denoted by l,m and n.
l=cosα,m=cosβ and n=cosγ
Here l=cos45o=21, m=cos60o=21 and let n=cosγ. Then,