Answer :

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,

l = cos 60°

m = cos 60°

n = cos α

By using the formula,

l2 + m2+n2 = 1

[As cos 60° value is ]

[As cos 45° ]

α = 45°

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

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