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Question
If a line makes angles 90°, 135°, 45° with the x, y and z axes respectively, find its direction cosines.
Solution 1
A-line makes 90° and 135°, 45°with x, y and z axes, respectively.
Therefore, Direction cosines of the line are cos 90°, cos135°, and cos45°
⇒ Direction cosines of the line are 0, `-(1)/sqrt(2),(1)/sqrt(2)`
Solution 2
Let the direction cosines of the line be l, m and n.
a = 90°, b = 135°, c = 45°
Now,
l = cos a = cos 90° = 0
m = cos b = cos 135° = `-1/sqrt2`
n = cos c = cos 45° = `1/sqrt2`
direction cosines of a line = `0, -1/sqrt2, 1/sqrt2`
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