Question:
If the direction ratios of two lines \(L_1\) and \(L_2\) are \((1,-2,2)\) and \((-2,3,-6)\) respectively, then the direction ratios of the line which is perpendicular to both \(L_1\) and \(L_2\) are?
If the direction ratios of two lines \(L_1\) and \(L_2\) are \((1,-2,2)\) and \((-2,3,-6)\) respectively, then the direction ratios of the line which is perpendicular to both \(L_1\) and \(L_2\) are?
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Use cross product of direction ratios to find a vector perpendicular to both lines.
Updated On: Jun 6, 2025
- \((1,-2,3)\)
- \((-2,3,5)\)
- \((6,2,-1)\)
- \((2,-1,3)\)
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The Correct Option is C
Solution and Explanation
Direction ratios of line perpendicular to both lines is the cross product of their direction ratios:
\[
(1,-2,2) \times (-2,3,-6) = ( (-2)(-6) - 2(3),\ 2(-2) - 1(-6),\ 1 . 3 - (-2)(-2) ) = (12 - 6, -4 + 6, 3 - 4) = (6, 2, -1).
\]
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