Find the angle between each of the following pairs of lines:
5, –12, 13; – 3, 4, 5

Solution

The direction-ratios of the two lines are 5, – 12, 13 and – 3, 4, 5.
Let θ be the angle between the lines.
$therefore space space cos space straight theta space equals space fraction numerator left parenthesis 5 right parenthesis thin space left parenthesis negative 3 right parenthesis space plus space left parenthesis negative 12 right parenthesis thin space left parenthesis 4 right parenthesis space plus space left parenthesis 13 right parenthesis thin space left parenthesis 5 right parenthesis over denominator square root of 5 plus 144 plus 169 end root space square root of 9 plus 16 plus 25 end root end fraction space equals space fraction numerator 15 minus 48 plus 65 over denominator 13 square root of 2 space 5 square root of 2 end fraction space equals space fraction numerator 2 over denominator 2 cross times 65 end fraction equals 1 over 65 therefore space straight theta space equals space cos to the power of negative 1 end exponent open parentheses 1 over 65 close parentheses$

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Three Dimensional Geometry

Find the angle between each of the following pairs of lines:
5, –12, 13; – 3, 4, 5

Some More Questions From Three Dimensional Geometry Chapter

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

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NCERT Sample Papers

Entrance Exams Preparation

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For Daily Free Study Material Join wiredfaculty

Three Dimensional Geometry

Find the angle between each of the following pairs of lines:5, –12, 13; – 3, 4, 5

Some More Questions From Three Dimensional Geometry Chapter

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

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Find the angle between each of the following pairs of lines:
5, –12, 13; – 3, 4, 5