Question

A line makes an angle of 60° with each of X-axis and Y-axis. Find the acute angle made by the line with Z-axis.

Answer 1

Given that, the line makes angles

• 60° with the x-axis.

• 60° with the y-axis.

Let the angle made by the line with z-axis be α.

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,

By using the formula,

l² + m² + n² = 1

Therefore, the angle made by the line with z-axis is 45°.