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Does the line x=y=0 lie in the plane z=0...

Does the line x=y=0 lie in the plane z=0.

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True or false The line x=y=z lies in the plane x-2y+z-1=0.

Find the equation of the image of the plane x-2y+2z-3=0 in plane x+y+z-1=0.

Prove that the line of section of the planes 5x+2y-4z+2=0 and 2x+8y+2z-1=0 is parallel to the plane 4x-2y-5z-2=0.

Prove that the line of section of the planes 2x-y+z=4 and 5x+7y+2z=0 meets the plane 3x+4y-2z+3=0 in a single point. Find the cooridnates of that point.

Find x and y if the point (x,-1,3), (3,y,1) and (-1,11,9) are collinear. Also, write down the vector equation of the line in which they lie. Further, find the point of intersection of this line and the plane x+y+z+1=0 .

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

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

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

Find the angle between the lines in which the planes: 3x-7y-5z=1, 5x-13y+3z+2=0 cut the plane 8x-11y+2z=0 .

PRADEEP PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXERCISE
  1. Find the intercepts of the plane 2x-3y+4z-24=0 on the cooridnate axes.

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  2. Find the distance of the plane x+y+z-sqrt3=0 from the origin.

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  3. Does the line x=y=0 lie in the plane z=0.

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  4. Name the surface represented by the equation 2x-3y=0.

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  5. Find the distance between the point (2,3,6) and (0,0,0).

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  6. Write down the coordinates of the mid point of the segment joining the...

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  7. If the direction ratios of a line <2,-1,-2> find the direction cosines...

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  8. find the vector equations of the line which is parallel to the vector ...

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  9. Find the direction cosines of the line passing through the points P(2,...

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  10. If a line makes an angles of 30^@, 60^@, 90^@ with the positive direct...

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  11. If the x - coordinate of a point P on the line joining points Q(2,2,1)...

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  12. Find the distance of the point whose position vector is 2hati+hatj-hat...

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  13. Find the position vector of a point A in space such thatvec(OA) is inc...

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  14. Parametric equations of a line are x=-1+2t, y=3-4t and z=2+t. find the...

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  15. Parametric equations a line are x=2-3t, y=-1+2t and z=3+t. write down ...

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  16. Vector equations of a line if vecr=3hati-6hatj+7hatk+lambda(2hati-hatj...

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  17. Vector equation of a plane is vecr.(2hati+4hatj-3hatk)=5. Write down t...

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  18. What is the distance of the point (-1,2,1) from the plane 2x-3y+4z+5=0...

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  19. Find p if the plane x+y-2z+6=0 is parallel to the plane px+3y-6z-1=0.

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  20. Write the equation to the locus of a point which is always at a fixed ...

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