If a line makes an angle of 60°, 150°, 45° with the positive x, y, z-axis respectively, find its direction cosines.

Category: QuestionsIf a line makes an angle of 60°, 150°, 45° with the positive x, y, z-axis respectively, find its direction cosines.
Editor">Editor Staff asked 11 months ago

If a line makes an angle of 60°, 150°, 45° with the positive x, y, z-axis respectively, find its direction cosines.
 
(a) –\(\frac{1}{2},-\frac{\sqrt{3}}{2},\frac{1}{\sqrt{2}}\)
 
(b) –\(\frac{1}{2},-\frac{\sqrt{3}}{2},-\frac{1}{\sqrt{2}}\)
 
(c) \(\frac{1}{2},-\frac{\sqrt{3}}{2},\frac{1}{\sqrt{2}}\)
 
(d) \(\frac{1}{2},\frac{\sqrt{3}}{2},-\frac{1}{\sqrt{2}}\)
 
I have been asked this question in class test.
 
This is a very interesting question from Direction Cosines and Direction Ratios of a Line in portion Three Dimensional Geometry of Mathematics – Class 12
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1 Answers
Editor">Editor Staff answered 11 months ago

Correct answer is (c) \frac{1}{2},-\frac{\sqrt{3}}{2},\frac{1}{\sqrt{2}}
 
Easiest explanation: Let l, m, n be the direction cosines of the line.
 
We know that, if α, β, γ are the angles that the line makes with the x, y, z-axis respectively, then
 
l=cos⁡α=cos⁡60°=\frac{1}{2}
 
m=cos⁡β=cos⁡150°=-\frac{\sqrt{3}}{2}
 
n=cos⁡γ=cos⁡45°=\frac{1}{\sqrt{2}}.