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Prove that if a plane has the intercepts...

Prove that if a plane has the intercepts a, b, c and it is at a distance p units
from the origin, then `(1)/a^2 + (1)/b^2+(1)/c^2 = (1)/p^2`

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V PUBLICATION-THREE DIMENSIONAL GEOMETRY-QUESTION BANK
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  2. Find the vector equation of the line passing through the point (1,2,-4...

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  3. Prove that if a plane has the intercepts a, b, c and it is at a distan...

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

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

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

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

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

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  9. 1, '-2,-2' are direction ratios of a line. What are its direction cosi...

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

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

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

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

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

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

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

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

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

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

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