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CBSE Class 12-science Answered



Show that the lines and are perpendicular.



Asked by Topperlearning User | 25 Feb, 2015, 08:55: AM
Expert Answer

The direction ratios of the first line are 3, – 2, 5 and the direction ratios of the second line are 1, – 1, -1. If the angle between the lines is, then

 
cos theta equals fraction numerator 3 cross times 1 plus open parentheses negative 2 close parentheses cross times open parentheses negative 1 close parentheses plus 5 open parentheses negative 1 close parentheses over denominator square root of 9 plus 4 plus 25 end root cross times square root of 1 plus 1 plus 1 end root end fraction
rightwards double arrow cos theta equals fraction numerator 5 minus 5 over denominator square root of 38 cross times square root of 3 end fraction
rightwards double arrow cos theta equals 0
rightwards double arrow cos theta equals cos 90 degree
rightwards double arrow theta equals 90 degree

Thus, the lines are perpendicular.
Answered by | 25 Feb, 2015, 10:55: AM
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