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If l(1), m(1), n(1) and l(2), m(2), n(2)...

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 them are `m_(1)n_(2) - n_(1)m_(2), n_(1)l_(2) - l_(1)n_(2), l_(1)m_(2) - m_(1)l_(2)`

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ARIHANT PUBLICATION-THREE-DIMENSIONAL GEOMETRY-Odisha Bureau.s Textbooks Solutions (Exercise 13(a))
  1. Show that the points (3,-2,4)(1,1,1) and (-1,4,-1) are collinear.

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  2. Show that points (0,1,2),(2,5,8),(5,6,6) and (3,2,0) from a parallelog...

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  3. Find the co-ordinates of the foot of the perpendicular from the point ...

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  4. Find the co-ordinates of the point where the perpendicular from the or...

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  5. Prove that the points P(3,2,-4),Q(5,4,-6) and R(9,8:-10) are collinea...

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  6. If P (1,y,z) lies on the line through (3,2,-1) and (-4,6,3) find y & z...

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  7. If A, B, C, D are the points (6,3,2), (3,5,7), (2,3,-1) and (3,5,-3) r...

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  8. The projection of a line segment overline(OP), through origin O, on th...

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  9. The projection of a line segment of x, y and z-axis respectively are 1...

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  10. If A, B, C are the points (1, 4, 2), (-2,1,2) and (2,-3,4) respectivel...

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  11. Find the acute angle between the lines passing through (-3, -1, 0), (2...

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  12. Prove that the measure of the angle between two main diagonals of a cu...

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  13. Prove that the measure of the angle between two main diagonals of a cu...

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  14. Find the angle which a diagonal of a cube makes with one of its edges.

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  15. Find the angle between the lines whose dcs. L, m, n are connected by t...

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  16. If the edges of a rectangular parallelopiped are of lengths a, b, c, t...

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  17. If l(1), m(1), n(1) and l(2), m(2), n(2)  are the direction cosines of...

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