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If A (6,-6,0), B(-1,-7,6), C (3,-4, 4) a...

If A (6,-6,0), B(-1,-7,6), C (3,-4, 4) and D (2,-9,2) be four points in space. Show that AB is perpendicular to CD.

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NAGEEN PRAKASHAN ENGLISH-THREE-DIMENSIONAL GEOMETRY -Exercise 11 A
  1. Find the direction cosines of that line whose direction ratios are as ...

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  2. Find the direction cosines of the line joining the following points : ...

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  3. Show that the point A(2,-3,-4), B(1,2,3), C(3,-8,-11) are collinear.

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  4. Find the angle between those lines whose direction ratios are as foll...

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  5. Find the angle between the following vectors : (i) veca = 2hati-6ha...

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  6. Show that the joint of the points (1,2,3), (4,5,7) is parallel to the ...

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  7. If A (6,-6,0), B(-1,-7,6), C (3,-4, 4) and D (2,-9,2) be four points i...

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  8. If vecr is a vector of magnitude 21 and has direction ratios 2, -3 an...

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  9. Find the angles which the following vectors, makes form the co-ordinat...

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  10. The pair of lines whose direction cosines are given by the equations 3...

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  11. The direction cosines of two lines satisfying the conditions l + m +...

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

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  13. Find the angle between any two diagonals of a cube.

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  14. Find the angle between two lines whose direction ratios are proport...

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  15. Find the angles of a triangle whose verties are A(3,2,1), B(35,2) and ...

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  16. If a line makes angles 90o," "135o," "45o with the x, y and z-axes ...

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  17. Find the direction cosines of a line which makes equal angles with ...

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  18. If a line has the direction ratios 18 , 12 , 4, then what are its ...

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

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  20. Find the direction cosines of the sides of the triangle whose vertice...

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