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.
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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