In this question why cant we take all the 3 angles to be equal and take ind value= 120 degree/
Find the direction cosines of a line which makes equal angles with the coordinate axes.

Question

In this question why cant we take all the 3 angles to be equal and
take ind value= 120 degree/
Find the direction cosines of a line which makes equal angles with
the coordinate axes

Ajanta Trivedi · Accepted Answer

Dear Ratna,
we can not take the angles as 120 deg as the sum of the angles made
with coordinate axes is not 360 deg

if a line makes equal angles with the coordinate axes, then
α=β=γ
and l=cosα, m=cosβ and n=cosγ
l2+m2+n2=1cos2α+cos2α+cos2α=13
cos2α=1⇒cos2α=13cosα=±13
thus the DC's of the line are ±13,±13,±13

hope this helps you

In this question why cant we take all the 3 angles to be equal and take ind value= 120 degree/Find the direction cosines of a line which makes equal angles with the coordinate axes.

In this question why cant we take all the 3 angles to be equal and take ind value= 120 degree/
Find the direction cosines of a line which makes equal angles with the coordinate axes.