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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