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Question
If a line makes angles of 90°, 135° and 45° with the x, y and z axes respectively, then its direction cosines are ______.
Options
`0, -1/sqrt(2), 1/sqrt(2)`
`-1/sqrt(2), 0, 1/sqrt(2)`
`1/sqrt(2), 0, -1/sqrt(2)`
`0, 1/sqrt(2), 1/sqrt(2)`
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Solution
If a line makes angles of 90°, 135° and 45° with the x, y and z axes respectively, then its direction cosines are `underlinebb(0, -1/sqrt(2), 1/sqrt(2))`.
Explanation:
l = cos α, m = cos β, n = cos γ
l = cos 90°, m = cos 135°, n = cos 45°
l = 0, m = `(-1)/sqrt(2)`, n = `1/sqrt(2)`
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