Find the direction ratios and the direction cosines of the lines joining the pairs of points:
(– 1, –1, –1), (2, 3, 4)

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Solution

The direction ratios of the line joining the points (–1, – 1, –1), (2, 3, 4) are 2 + 1, 3 + 1, 4 + 1 i.e. 3, 4, 5.
Dividing each by

square root of left parenthesis 3 right parenthesis squared plus left parenthesis 4 right parenthesis squared plus left parenthesis 5 right parenthesis squared end root space equals space square root of 9 plus 16 plus 25 end root space equals space square root of 50 space equals space 5 square root of 2 comma

we get, the direction cosines of the line as

fraction numerator 3 over denominator 5 square root of 2 end fraction comma space fraction numerator 4 over denominator 5 square root of 2 end fraction comma space fraction numerator 5 over denominator 5 square root of 2 end fraction.

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