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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Solution

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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