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Find the equation of the plane through the line of intersection of the planes x + y + z = 1 and 2x + 3y + 4z = 5 which is perpendicular to the plane x - y + z = 0.

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Find the equation of the plane passing through the intersection of the planes 2x - 3y + z-4 = O and x-y + 2 + 1 = 0 and perpendicular to the plane x + 2y - 3z + 6 = 0.

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.

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).

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).

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..........

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The direction of the line of instersection of the planes 3x-z = 5 and 2y + x+z = 3 is ....

KUMAR PRAKASHAN-THREE DIMENSIONAL GEOMETRY-PRACTICE PAPER -11
  1. Find the direction cosines of a line which makes equal angles with the...

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  2. Find the direction cosines of the line passing through the two points ...

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  3. The foot of perpendicular drawn from the origin to the plane 2x + 3y +...

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  4. The plane 2x+3y+6z = 15 makes an angle of measure .........with Y-axis...

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  5. The symmetric from of the equation of the line x + y -z = 1 and 2x -3y...

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  6. A variable plane makes with the co-ordinates plane, tetrahedron of con...

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  7. Find the angle between the line (x+1)/(2)=y/3=(z-3)/(6) and the plane ...

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  8. Find the distance of the point (3,-2,1) from the plane 2x-y+2z + 3 = 0...

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

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  10. Find the vector and the cartesian equations of the line that passes th...

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  11. Find the shortest distance between the lines (x+1)/(7)=(y+1)/(-6)=(...

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  12. Find the equation of the plane through the line of intersection of the...

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

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

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  15. A line makes the angle alpha, beta , gamma and delta with the diagonal...

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  16. Find the image of the point (1,3,4) in the plane 2x-y +z = -3.

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