Find the angle between the pair of lines with direction ratios 2, 6, 3 and 1, 2, 2.

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Solution

The direction ratios of two lines are 2, 6, 3 and 1, 2, 2.
Let θ be the angle between the lines

therefore space space space space space cos space straight theta space equals space fraction numerator left parenthesis 2 right parenthesis thin space left parenthesis 1 right parenthesis space plus space left parenthesis 6 right parenthesis thin space left parenthesis 2 right parenthesis space plus space left parenthesis 3 right parenthesis thin space left parenthesis thin space 2 right parenthesis over denominator square root of 4 plus 36 plus 9 end root space square root of 1 plus 4 plus 4 end root end fraction space equals space fraction numerator 2 plus 12 plus 6 over denominator square root of 49 space square root of 9 end fraction space equals space fraction numerator 20 over denominator 7 cross times 3 end fraction space equals space 20 over 21 therefore space space space space space space space space space space straight theta space equals space cos to the power of negative 1 end exponent open parentheses 20 over 21 close parentheses

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