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

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

therefore space space straight l space equals cos space 45 degree space equals fraction numerator 1 over denominator square root of 2 end fraction comma space straight m space equals space cos space 45 degree space equals space fraction numerator 1 over denominator square root of 2 end fraction comma space straight n space equals space cos space 60 degree space equals space 1 half

These values of l, m, n do not satisfy the selection l² + m² + n² = 1 as

open parentheses fraction numerator 1 over denominator square root of 2 end fraction close parentheses squared plus space open parentheses fraction numerator 1 over denominator square root of 2 end fraction close parentheses squared plus space open parentheses 1 half close parentheses squared space equals space 1 half plus 1 half plus 1 fourth space equals 5 over 4 not equal to 1

∴ given angles cannot be the direction angles of a line.

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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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