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

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Let l, m, n be the direction cosines of the line with direction angles 45°. 60°, 120°
∴ l = cos 45°

equals space fraction numerator 1 over denominator square root of 2 end fraction comma space space straight m space equals space cos space 60 degree space equals 1 half comma space space straight n space equals cos space 120 degree space equals space cos space left parenthesis 180 degree minus 60 degree right parenthesis space equals space minus cos space 60 degree space equals negative 1 half

therefore space space space straight l squared plus straight m squared plus straight n squared space equals space 1 half plus 1 fourth plus 1 fourth space equals space fraction numerator 2 plus 1 plus 1 over denominator 4 end fraction space equals 4 over 4 space equals 1

∴ a line can have the given angles as direction angles.

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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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