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Question
If a line makes angles 90°, 135°, 45° with the X, Y, and Z axes respectively, then its direction cosines are _______.
(A) `0,1/sqrt2,-1/sqrt2`
(B) `0,-1/sqrt2,-1/sqrt2`
(C) `1,1/sqrt2,1/sqrt2`
(D) `0,-1/sqrt2,1/sqrt2`
Solution
(D) `0,-1/sqrt2,1/sqrt2`
Let α, β, γ be the angles made by the line with positive directions of X, Y, Z axes respectively.
α = 90°, β = 135°, γ = 45°
l = cos 90°, m = cos 135°, n = cos 45°
Now, m = cos 135° = cos(180° – 45°)
=`-cos45^@=-1/sqrt2`
`l=0, m=-1/sqrt2, n=1/sqrt2`
Direction cosines of the line are `0,-1/sqrt2,1/sqrt2`
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