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

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Find the distance of the point (2,1,0) from the plane 2x+y+2z+5=0.

The distance of the point (2,1,-1) from the plane x-2y+4z=9 is :

Find the distance of a point (6,0,0) from the plane 2x-3y+6z-2=0 .

Find the distance of the point (1, - 2, 3) from the plane x - y + z = 5 , measured parallel to the line x/2=y/2=z/-6

Find the coordinates of the foot of the perpendicular and the perpendicular distance of the point P (3, 2, 1) from the plane 2x - y + z + 1 = 0. Find also, the image of the point in the plane.

Find the distance of the point (1,-2,3) from the plane x-y+z=5 measured parallel to the line (x)/(2)=(y)/(3)=(z)/(-6) .

If the distance of the point P(1,-2,1) from the plane x+2y-2z=alpha , where alpha>0 , is 5, then the foot of the perpendicular from P to the plane is:

Find the co-ordinates of the foot of the perpendicular distance of the point P(3,2,1) from the plane 2x-y+z+1=0 . Find also , the image of the point in the plane.

Find the distance of the point (1, 0, -3) from the plane x-y-z=9 measured parallel to the line (x-2)/(2)=(y+2)/(3)=(z-6)/(-6) .

Find the co-ordinates of the foot of the perpendicular and the perpendicualr distance of the point (1,3,4) from the plane 2x-y+z+3=0 . Find also, the image of the point in the plane.

PRADEEP PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXERCISE
  1. Vector equations of a line if vecr=3hati-6hatj+7hatk+lambda(2hati-hatj...

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

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

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

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

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  6. Find the vector equations to the locus of a point whose distance from ...

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  7. If the line drawn from the point (-2,-1,-3) meets a plane at right ang...

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  8. Write the distance of the plane 2x-y+2z+1=0 from the origin.

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  9. Write the direction of cosines of the line joining the poidnts (1,0,0)...

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  10. Write the vector equations of the plane throught the point (a,b,c) and...

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  11. If the cartesian equations of a line are : (3-x)/5=(y+4)/7=(2z-6)/4, w...

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  12. Distance of the point (2,5,-3) from the plane vec r.(6hat i-3 hat j+2 ...

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  13. Write down the direction cosines of the line whose equations are 5x-3=...

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  14. Write the sum of intercepts cut off by the plane vecr*(2hati+hatj-hatk...

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  15. If a line angles 90^@, 135^@, 45^@ with the positive x,y and z axis re...

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  16. Find the direction cosines of a line which makes equal angles with the...

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  17. If a line has the direction ratios –18, 12, – 4, then what are its dir...

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  18. Show that the points (2, 3, 4), (– 1, – 2, 1), (5, 8, 7) are collinear...

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  19. Find the direction cosines of the sides of the triangle whose vertices...

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  20. show that the three lines with direction cosines <12/13,-3/13,-4/13>, ...

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