Class 12

Math

3D Geometry

Three Dimensional Geometry

A line makes angles $90_{o},135_{o}$ and $45_{o}$ with positive directions of x-axis, y-axis and z-axis respectively. What are the direction cosines of the line?

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 $n=cosγ$

Direction cosines of the line are $cos90_{o},cos135_{o},cos45_{o}$

i.e. ${0,2 −1 ,2 1 }$