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Find the distance between the parallel p...

Find the distance between the parallel planes `vecr.(2hati-3hatj+6hatk)=5` and `vecr.(6hati-9hatj+18hatk)+20=0`

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The correct Answer is:
`5/3`
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Find the angle between the planes whose vector equations are vecr.(2hati+2hatj-3hatk)=5 and vecr.(3hati-3hatj+5hatk)=3 .

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Find the vector equation of the line passing through (1, 2, 3) and parallel to the planes vecr.(hati-hatj+2hatk)=5 and vecr.(3hati+hatj+hatk)=6

Find the shortest distance between the lines vecr=(hati+2hatj+hatk)+lambda(hati-hatj+hatk) and vecr=2hati-hatj-hatk+mu(2hati+hatj+2hatk) .

Find the Cartesian equation of the following planes : (a) vecr.(hati+hatj-hatk)=2 (b) vecr.(2hati+3hatj-4hatk)=1 (c) vecr.((s-2t)hati+(3-t)hatj+(2s+t)hatk)=15

Find the equation of the plane passing through the line of intersection of the planes vecr.(hati+hatj+hatk)=1 and vecr.(2hati+3hatj-hatk)+4=0 and parallel to X- axis.

Find the distance between the lines l_1 and l_2 given by vecr=hati+2hatj-4hatk+lambda(2hati+3hatj+6hatk) and vecr=3hati+3hatj-5hatk+mu(2hati+3hatj+6hatk) .

Find the distance of a point (2, 5, -3) from the plane vecr.(6hati-3hatj+2hatk)=4

Find the cartesian equation of the plane| through the intersection of the planes vecr.(2hati+6hatj)+12=0 and vecr.(3hati-hatj+4hatk)=0 which are at a unit distance from the origin.

Find the image of the point (1, 3, 4) in the plane vecr.(2hati-hatj+hatk)+3=0

KUMAR PRAKASHAN-THREE DIMENSIONAL GEOMETRY-PRACTICE WORK
  1. If the points (1, 1, lambda) and (-3, 0, 1) be equidistant from the pl...

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  2. Find the distance between the parallel planes x + y - z + 4 = 0 and x ...

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  3. Find the distance between the parallel planes vecr.(2hati-3hatj+6hatk...

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  4. If the distance of the plane x - y + z + lambda = 0 from the point (1,...

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  5. The direction cosines of two lines are 1, -2,-2 and 0, 2, 1. Find the ...

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  6. The direction cosines of two lines are given by the following equation...

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  7. Show that the line passing through the points (4, 7, 8) and (2, 3, 4) ...

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  8. Show that the line passing through (1, -1, 2) and (3, 4, -2) is perpen...

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  9. Find the angle between the lines (5-x)/(-2)=(y+3)/(1)=(1-z)/(3) and x/...

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  10. Show that the lines (x-5)/(7)=(y+2)/(-5)=z/1 and x/1=y/2=z/3 are perpe...

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  11. Find the co-ordinates of the point where the line (x+1)/(2)=(y+2)/(3)=...

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  12. Find the co-ordinates of the point where the line through A(3, 4, 1) a...

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  13. Find the coordinates of the foot of perpendicular drawn from the point...

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  14. Find the foot of perpendicular from the point (0, 2, 3) on the line (x...

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  15. Find the image of the point (3, 5, 3) with respect to the line x/1=(y-...

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  16. Find the equation of the plane passing through the points (1, 2, 3) an...

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

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  18. Find the equation of the plane passing through the point (3, 4, -1) an...

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

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  20. If the points (1, 1, lambda) and (-3, 0, 1) be equidistant from the pl...

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