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If a line makes angles 90º, 135º, 45º with the X, Y and Z axes respectively, then find its direction cosines. |
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Answer» Let l, m, n be the direction cosines of the line. Then l = cos α, m = cos β, n = cos γ Here, α = 90°, β = 135° and γ = 45° ∴ l = cos 90° = 0 m = cos 135° = cos (180° – 45°) = -cos 45° \(= -\frac{1}{\sqrt{2}}\) and n = cos 45° \(= \frac{1}{\sqrt{2}}\) ∴ the direction cosines of the line are 0, \(-\frac{1}{\sqrt{2}},\) \(\frac{1}{\sqrt{2}}\) |
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