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find the length and the foot of perpendicular drawn from the point (1,1,2) to the plane
`vecr.(2hati-2hatj+4hatk)+5=0`.

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Find the coordinates of the foot of the perpendicular and the length of the perpendicular drawn from the point P(5,4,2) to the line vecr=(-hati+hatj+hatk)+lambda(2hati+hatj-hatk) . Also find the image of P in this line.

Find the co ordinates of the foot of perpendicular and the length of the perpendicular drawn from the point P(5,4,2) to the line : vecr=-hati+3hatj+hatk+lambda(2hati+3hatj-hatk) . Also find the image of P in this line.

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A line passing through the point A with position vector veca=4hati+2hatj+2hatk is parllel to the vector vecb=2hati+3hatj+6hatk .Find the length of the perpendicular drawn on this line from a point P with position vector vecr_1=hati+2hatj+3hatk .

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PRADEEP PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXERCISE
  1. If the lines: (x-1)/-3=(y-2)/(-2k)=(z-3)/2 and (x-1)/k=(y-2)/1=(z-3)/5...

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  2. Find the length and the foot of the perpendicular from the point (7, 1...

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  3. find the length and the foot of perpendicular drawn from the point (1,...

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  4. Find image of point (1, 3, 4) in the plane 2x-y+z+3=0.

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  5. Find the image of the point hati+3hatj+4hatk in the plane vecr.(2hati-...

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  6. Find the length and foot of perpendicular drawn from the point (3,2,1)...

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  7. The image of the line (x-1)/3=(y-3)/1=(z-4)/(-5) in the plane 2x-y+z...

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  8. Find the projection of the line (x-1)/2=(y+1)/-1=(z-3)/4 in the plane ...

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  9. Find the distance of the line (x+1)/-3=(y-3)/2=(z-2)/1 in the plane x+...

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  10. The image of the line (x-1)/3=(y-3)/1=(z-4)/(-5) in the plane 2x-y+z...

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  11. Find the ratio in which the plane ax+by+cz+d=0 divides the join of the...

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  12. Show that the lines (x-a+d)/(alpha-delta) = (y-a)/alpha = (z-a-d)/(alp...

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  13. Find the angle between the planes 2x-3y+4z=1 and -x+y=4.

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  14. Find the angle between the planes: vecr.(hati+hatj)=1 and vecr.(hati+h...

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  15. Find the angle between the two planes 3x-6y+2z = 7 and 2x+2y-2z = 5

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  16. Show that the plane passing through the points (1,1,1), (1,-7,1) and (...

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  17. Find the equation of the plane passing through the points (1,-1,2) and...

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  18. Find the equation of the plane passing through the points (-1,1,1) and...

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  19. Find the equation of the plane passing through the line (x-1)/2=(y+1)/...

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  20. Obtain the equation of the plane passing through the point (1,-3,-2) a...

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