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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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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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The direction ratios of the line joining the points (–2, 1, 0) , (3, 2,1) are 3 + 2, 2 – 1, 1 – 0 i.e. 5, 1, 1.
Dividing each by

square root of left parenthesis 5 right parenthesis squared plus left parenthesis 1 right parenthesis squared plus left parenthesis 1 right parenthesis squared end root space equals space square root of 27 space equals space 3 square root of 3 comma

we get the direction cosines of the line as

fraction numerator 5 over denominator 3 square root of 3 end fraction comma space fraction numerator 1 over denominator 3 square root of 3 end fraction comma space fraction numerator 1 over denominator 3 square root of 3 end fraction

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