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If l1, m1, n1, and l2, m2, n2 are the di...

If `l_1, m_1, n_1`, and `l_2, m_2, n_2` are the direction cosines of two mutually perpendicular lines, show that the direction cosines of the line perpendicular to both of these are
`m_1n_2-m_2n_1,n_1l_2-n_2l_1,l_1m_2-l_2m_1`

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The correct Answer is:
`therefore` The direction cosine of the line L are
`m_1n_2-m_2n_1,n_1l_2-n_2l_1,l_1m_2-l_2m_1`
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KUMAR PRAKASHAN-THREE DIMENSIONAL GEOMETRY-MISCELLANEOUS EXERCISE-11
  1. Show that the line joining the origin to the point (2, 1, 1) is perpen...

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  2. If l1, m1, n1, and l2, m2, n2 are the direction cosines of two mutuall...

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  3. Find the angle between the lines whose direction ratios are a, b, c an...

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  4. Find the equation of a line parallel to X- axis and passing through th...

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  5. If the coordinates of the points A, B, C, D be (1, 2, 3), (4, 5, 7), (...

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  6. If the lines (x-1)/(-3)=(y-2)/(2k)=(z-3)/(2) and (x-1)/(3k)=(y-1)/(1)=...

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  7. Find the vector equation of the line passing through (1, 2, 3) and per...

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  8. Find the equation of the plane passing through (a, b, c) and parallel ...

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  9. Find the shortest distance between lines vecr=6hati+2hatj+2hatk+la...

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  10. Find the coordinates of the point where the line through (5, 1, 6) and...

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  11. Find the coordinates of the point where the line through (5, 1, 6) and...

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  12. Find the coordinates of the point where the line through (3,--4,-5) an...

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  13. Find the equation of the plane passing through the point (-1, 3, 2) an...

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  14. If the points (1, 1, p) and (-3, 0, 1) be equidistant from the plane v...

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  15. Find the equation of the plane passing through the line of intersectio...

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  16. If O be the origin and the coordinates of P be (1, 2, - 3), then find ...

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  17. Find the equation of the plane which contains the line of intersection...

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  18. Find the distance of the point (-1, -5, -10) from the point of interse...

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  19. Find the vector equation of the line passing through (1, 2, 3) and par...

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  20. Find the vector equation of the line passing through the point (1, 2, ...

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