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Prove that the lines (x+4)/3=(y+6)/5=(z...

Prove that the lines `(x+4)/3=(y+6)/5=(z-1)/(-2)` and `3x-2y+z+5=0=2x+3y+4z-4` are co-planar.

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Find the shortest distance between the lines (x-1)/(2) = (y-2)/(3) = (z-3)/(4) and (x-2)/( 3) = (y-3)/(4) = (z-5)/(5)

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ARIHANT PRAKASHAN-THREE DIMENSIONAL GEOMETRY -TOPIC -3- PRACTICE QUESTIONS
  1. Obtain the equation of the line through the point (1, 2, 3) and parall...

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  2. Find the point where the line (x-2)/1=y/(-1)=(z-1)/2 meets the plane 2...

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  3. Prove that the lines (x+4)/3=(y+6)/5=(z-1)/(-2) and 3x-2y+z+5=0=2x+3y...

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  4. Find the perpendicular distance of the point (-1,3,9) from the line (x...

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  5. Using the method of elemination find the symmetrical form of equation ...

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  6. Find the value of r, if the line  (x-1)/(1) = (y+2)/(3) = (z-1)/(-1) =...

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

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  8. Determine the symmetric form of the equation to the line of intersecti...

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  9. Find the equation of the plane passing through the line x = y = z and ...

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  10. Find the intersection of the line passing through the points (3, -2, 1...

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  11. Prove that the lines (x + 3)/(2) = (y + 5)/(3) = (z - 7)/(-3) and (x +...

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  12. Find the equation of the straight line which passes through the point ...

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  13. Find the angle between the pair of lines (x+3)/(3) = (y-1)/(5) = (z+...

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  14. Find the shortest distance between the lines  (x-3)/(1) = (y - 5)/(-2)...

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  15. Find the angle between the plane x+y+4=0 and the line (x+3)/2=(y-1)/1=...

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  16. Find the equation of the plane through (6,3,1) and (8,-5,3) parallel t...

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  17. Find the shortest distance between the lines (x - 3)/(3) = (y - 8)/(-1...

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  18. Show that the line joining the points (0,2,-4) and (-1,1-2) and the l...

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  19. Find the distance of the point (1,-2,3) from the plane x-y+z=5, measur...

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  20. Find a symmetric form of the equation to the lines x +2y-z-2= 0 and 2x...

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