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Question
If a line makes angles 90° and 60° respectively with the positive directions of x and y axes, find the angle which it makes with the positive direction of z-axis.
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Solution
Let the direction cosines of the line be l, m and n.
We know that l2 + m2 + n2 = 1.
Let the line make angle θ with the positive direction of the z-axis.
α=90°, β=60°, γ=Θ
So, cos290°+cos260°+cos2θ=1
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