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Three Dimensional Geometry

Question

If a line makes angles 90°, 135°, 45° with x, y and z-axes respectively, find its direction cosines.

Solution

Let l, m, n be the direction cosines of the line with direction angles 90°, 135°, 45°.

therefore space space straight l space equals space cos space 90 degree space equals space 0 comma space space space straight m space equals space cos space 135 degree space equals space cos space left parenthesis 180 degree minus 45 degree right parenthesis space equals space minus cos space 45 degree space equals space minus fraction numerator 1 over denominator square root of 2 end fraction comma

straight n space equals space cos space 45 degree space equals space fraction numerator 1 over denominator square root of 2 end fraction

therefore space space

direction cosines are 0,

negative fraction numerator 1 over denominator square root of 2 end fraction comma space fraction numerator 1 over denominator square root of 2 end fraction.

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