If a line makes a

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°.