If a line is perpendicular to z axis and makes an angle 40 degree with y axis then find the - Maths - Introduction to Three Dimensional Geometry

Question

If a line is perpendicular to z axis and makes an angle 40 degree
with y axis then find the angle it makes with the X axis

Varun.Rawat · Accepted Answer

Let α, β and γ be the angles made by the required line with x-axis, y-axis and z-axis
Now, α = ? ; β = 40°; γ=90°Now, direction cosines of the line are l,m,n and given by :l = cos α m = cos β = cos 40n = cos 90 = 0Also, l2+m2+n2 = 1⇒cos2α + cos240 + 0 = 1⇒cos2α = 1 - cos240⇒cos2α = sin240⇒cos2α = sin290-50⇒cos2α = cos250⇒α = 50°

If a line is perpendicular to z axis and makes an angle 40 degree with y axis then find the angle it makes with the X axis