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Prove that the lines whose direction cos...

Prove that the lines whose direction cosines are given by
al+bm+cn=0, fmn+gnl+hlm=0 are
parallel if `a^2f^2+b^2g^2+c^2h^2-2(bcgh+cahf+abfg)=0`.

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PRADEEP PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXERCISE
  1. Prove that the lines whose direction cosines are given by al+bm+cn=0, ...

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  2. Find the points on z-axis which are at a distance of sqrt21 from the p...

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  3. Find k so that the distance between the points (7, 1, - 3) and (4,5, k...

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  4. Find the point on x-axis which is equidistant from the point (1,3,2) a...

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  5. Find the point which is equidistant from the points (a,0,0),(0,b,0),(0...

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  6. Show that the points (2,4,3),(4,1,9) and (10,-1,6) are the vertices of...

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  7. Find the locus of a point which is equidistant from the points (3,2,1...

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  8. Find the point in the XY-plane which is equidistant from the points (2...

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  9. Prove that the point A (0,0,0),B(2,0,0),C(1,sqrt3,0) and D(1,1/sqrt3, ...

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  10. Find the coordinates of the point which divides the join of the points...

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  11. Find the points on the line segment PQ situated at 2/3 of the distan...

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  12. Find the points on the line segment PQ situated at 2/3 of the distan...

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  13. If A and B are two points whose position vectors are 3hati+2hatj-2hatk...

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  14. If A and B are two points whose position vectors are 3hati+2hatj-2hatk...

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  15. Find the coordinates of the point which is three fifth of the way (3,4...

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  16. Find the ratio in which the line segment joining : (1,2,3) and (-3,4,-...

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  17. If A and B are the points (-3,4,-8) and (5,-6,4) respectively, find th...

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  18. Using section formula, prove that the three points (-2,3,5),(1,2,3) an...

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  19. Show that the points : (4, 7, 8), (2, 3, 4), (- 1, - 2, 1), (1, 2, 5) ...

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  20. Using vectors, show that the medians of a triangle are concurrent.

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  21. Prove that the points A(5,0,2), B(2,-6,0),C(4,-9,6) and D(7,-3,8), tak...

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