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Find the coordinates of the point where the line through (3,--4,-5) and (2, -3, 1) crosses the plane 2x + y + z = 7.

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The correct Answer is:
`therefore` The required point is P(x,y,z)=(1,-2,7).
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KUMAR PRAKASHAN-THREE DIMENSIONAL GEOMETRY-MISCELLANEOUS EXERCISE-11
  1. Find the equation of a line parallel to X- axis and passing through th...

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  2. If the coordinates of the points A, B, C, D be (1, 2, 3), (4, 5, 7), (...

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  3. If the lines (x-1)/(-3)=(y-2)/(2k)=(z-3)/(2) and (x-1)/(3k)=(y-1)/(1)=...

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  4. Find the vector equation of the line passing through (1, 2, 3) and per...

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  5. Find the equation of the plane passing through (a, b, c) and parallel ...

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  6. Find the shortest distance between lines vecr=6hati+2hatj+2hatk+la...

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  7. Find the coordinates of the point where the line through (5, 1, 6) and...

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  8. Find the coordinates of the point where the line through (5, 1, 6) and...

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  9. Find the coordinates of the point where the line through (3,--4,-5) an...

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  10. Find the equation of the plane passing through the point (-1, 3, 2) an...

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  11. If the points (1, 1, p) and (-3, 0, 1) be equidistant from the plane v...

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  12. Find the equation of the plane passing through the line of intersectio...

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  13. If O be the origin and the coordinates of P be (1, 2, - 3), then find ...

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  14. Find the equation of the plane which contains the line of intersection...

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  15. Find the distance of the point (-1, -5, -10) from the point of interse...

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  16. Find the vector equation of the line passing through (1, 2, 3) and par...

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  17. Find the vector equation of the line passing through the point (1, 2, ...

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  18. Prove that if a plane has the intercepts a, b, c and is at a distance ...

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  19. Distance between the two planes : 2x + 3y + 4z = 4 and 4x + 6y + 8z = ...

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  20. The planes : 2x – y + 4z = 5 and 5x – 2.5 y + 10 z = 6 are

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