Question

Find the direction cosines of the line passing through the two points (–2, 4, –5) and (1, 2, 3).

Solution

The direction ratios of the line joining the points (–2, 4, –5) and (1. 2, 3) are
1 + 2, 2 – 4, 3 + 5 i.e. 3, – 2, 8.
Dividing each by $square root of left parenthesis 3 right parenthesis squared plus left parenthesis negative 2 right parenthesis squared plus left parenthesis 8 right parenthesis squared end root space equals space square root of 9 plus 4 plus 64 end root space equals space square root of 77 comma$ we get the direction cosines of the line as $fraction numerator 3 over denominator square root of 77 end fraction comma space minus fraction numerator 2 over denominator square root of 77 end fraction comma space fraction numerator 8 over denominator square root of 77 end fraction.$

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Three Dimensional Geometry

Find the direction cosines of the line passing through the two points (–2, 4, –5) and (1, 2, 3).

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

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