If a line makes angle 90° and 60° respectively with positive directions of x an y axe, find the angle which it makes with the positive direction of z-axis.
Given a line makes,
• an angle of 90° with x-axis
• an angle of 60° with y-axis
So, let the angle made by the line with z-axis is θ
Now, as per the relation between direction cosines of a line, l2 + m2+n2 = 1 where l,m,n are the direction cosines of a line from x-axis, y-axis and z-axis respectively.
From the problem,
l = cos 90° = 0
m = cos 60° 
n = cos θ
By using the formula,
l2 + m2+n2 = 1
As the angle made by the line with positive z-axis, so the cosine angle is positive.
Therefore, cos θ =
Hence θ = 30°.
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