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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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Can a directed line have direction angles 45°, 60°, 120°?

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3. Can a directed line have direction angles 45°, 45°, 60°?

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A line makes an angle of $straight pi over 4$ with each of y-axis and z-axis. Find the angle made by it with x-axis.

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5. Find the direction cosines of x, y and z-axis.

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6. Find the direction-cosines of a line which makes equal angles with the axes. How many such lines are there?

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If a line has direction ratios 2, -1, -2, determine its direction cosines.

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If a line has direction ratios 2, -1, -2, determine its direction cosines.

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9. If a line has the direction ratios – 18, 12, – 4. then what are its direction cosines?

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10. Find the direction ratios and the direction cosines of the lines joining the pairs of points:
(–2, 1, 0), (3, 2, 1).

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