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Given direction ratios   and  . Thus the angle between the lines A is given by; a Thus, the angle between the lines is .
Given that  are the direction cosines of two mutually perpendicular lines. Therefore, we have the relation:                               .........................(1)          .............(2) Now, let us assume  be the new direction cosines of the lines which are perpendicular to the line with direction cosines. Therefore we have,  Or,      ......(3) So, l,m,n are the direction cosines of the...
We can assume the line joining the origin, be OA where  and the point  and PQ be the line joining the points  and . Then the direction ratios of the line OA will be   and that of line PQ will be So to check whether line OA is perpendicular to line PQ then, Applying the relation we know, Therefore OA is perpendicular to line PQ.