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If points 'P, Q' are '(2,3,-6)' and '(3,...

If points 'P, Q' are '(2,3,-6)' and '(3,-4,5)', find the angle that OP makes with OQ.

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V PUBLICATION-THREE DIMENSIONAL GEOMETRY-QUESTION BANK
  1. Prove that if a plane has the intercepts a, b, c and it is at a distan...

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  2. Distance between the two planes: '2 x+3 y+4 z=4' and '4 x+6 y+8 z=(12)...

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  3. The planes '2 x-y+4 z=5' and '5 x-2.5 y+10 z=6' are

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  4. Can a line have direction angles 45^circ, 60^circ, 135^circ?

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  5. A line makes angles of 45^circ and 60^circ with the positive axes of X...

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  6. Find the direction cosine of a line which makes equal angles with the...

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  7. 1, '-2,-2' are direction ratios of a line. What are its direction cosi...

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  8. Find d.c.'s of the line passing through the points 'P(4,3,-5)' and 'Q(...

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  9. A line passes through the points (6,-7,-1) and (2,-3,1) Find the direc...

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  10. Find the angle between the lines whose diréction ratios are '2,3,4' an...

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  11. Find the obtuse angle between the lines with direction ratios '3,-6,2'...

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  12. If points 'P, Q' are '(2,3,-6)' and '(3,-4,5)', find the angle that OP...

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  13. If A, B, C, D are the points (3,4,5),(4,6,3),(-1,2,4) and (1,0,5), fin...

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  14. Find the coordinates of foot of perpendicular drawn from the point (1,...

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  15. Prove that the Iine joining the midpoints of the two sides of a triang...

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  16. The cartesian equations of a line are 6 x-2=3 y+1=2 z-2. Find directi...

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  17. Find the shortest distance between the lines: vecr=3 hati+8 hatj+3 h...

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  18. Find the shortest distance between the lines vecr = (1-t)hati+(t-2)hat...

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  19. Find the angle between the line (x-2)/3=(y+1)/-1=(z-3)/-2 and the plan...

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  20. Find the length and foot of the perpendicular from the point (7,14,5)...

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