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Find the equation of the plane passing through the intersection of the planes x + 2y + 3z-4 = 0 and 2x + y - Z+ 5 = 0 and perpendicular to the plane 5x + 3y + 6z + 8 = 0.

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The correct Answer is:
51x + 15y - 50z + 173 = 0
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Find the equation of the plane through the intersection of the planes 3x – y + 2z – 4 = 0 and x + y + z- 2 = 0 and the point (2, 2, 1).

Find the equation of the line passing through the point (3, 0, 1) and parallel to the planes x + 2y = 0 and 3y – z = 0.

The equation of the plane passing through the intersection of the planes 2x-5y = z = 3 and x+y+4z = 5 and parallel to the plane x+3y + 6z = 1 is x + 3y + 6z = k is..........

Find the equation of the plane containing the line of intersection of the plane x + y + z-6 = 0 and 2x + 3y + 4z + 5 = 0 and passing through the point (1, 1, 1).

The equation of the plane through the intersection of the planes x+y+z=1 and 2x+3y-z+4 = 0 and parallel to x-axis is

Find the equation of the plane through the intersection of the planes x+3y+6=0 and 3x-y-4z=0 , whose perpendicular distance from the origin is unity.

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KUMAR PRAKASHAN-THREE DIMENSIONAL GEOMETRY-PRACTICE WORK
  1. Find the equation of the plane containing the line of intersection of ...

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  2. Find the equation of the plane through the line of intersection of vec...

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  3. Find the equation of the plane passing through the intersection of the...

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  4. Find the cartesian equation of the plane| through the intersection of ...

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  5. Find the equation of the plane passing through the intersection of the...

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  6. In the following cases, determine whether the given planes are paralle...

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  7. If the planes vecr.(hati+2hatj-3hatk)=7 and vecr.(lambdahati+2hatj-7ha...

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  8. Find the distance of the point (2, 1, 0) from the plane 2x + y + 2z + ...

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

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

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

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

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

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

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

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

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

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

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

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