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Prove that the points P(1,2,3),(3,1,7) a...

Prove that the points P(1,2,3),(3,1,7) and (7,-1,15) are collinear.

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KUMAR PRAKASHAN-THREE DIMENSIONAL GEOMETRY-PRACTICE WORK
  1. If a line has direction cosines 2/3,-1/3,-2/3, then find its direction...

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  2. Find the direction cosines of the line joining the two points P(-2, 4,...

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  3. Prove that the points P(1,2,3),(3,1,7) and (7,-1,15) are collinear.

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  4. Find the vector equation of the line through the point whose position ...

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  5. The cartesian equation of a line are 6x - 2 = 3y + 1 = 2z - 2. Find it...

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  6. Find the direction cosines of the line (x-2)/(2)=(2y-5)/(-3),z=-1. Als...

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  7. If the points A(-1, 3, 2), B(-4, 2, -2) and C(5, 5, lambda) are collin...

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

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  9. Find the vector equation of a line passing| through (2, -1, 1) and par...

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  10. squareABCD is a parallelogram. The position vectors of the points A, B...

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

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  12. Find the angle between the lines vecr = (3 + lambda)hati + 2(1 + l...

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  13. Find the angle between the lines whose direction cosines are given by ...

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  14. Show that the lines (x-2)/(3)=(y+1)/(-2)=2 and (x-1)/(1)=(2y+3)/(3)=(z...

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  15. Prove that if the lines x = ay + b, z = cy + d and x = a'y + b', z = c...

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  16. Find the values of p so that the lines (1-x)/(3)=(7y-14)/(2p)=(z-3...

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  17. Find the shortest distance between the lines vecr =(8+3lambda) hati - ...

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  18. Find the shortest distance between the lines vecr=(4hati-hatj)+lam...

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

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

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