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Find the equation of the plane containin...

Find the equation of the plane containingg the lines: `vecr=hati+hatj+lambda(hati+2hatj-hatk) and vecr=hati+hatj+mu(-hati+hatj-2hatk)`. Find the distance of this plane from origin and also from the point (1,1,1).

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Find the shortest distance between the lines : vecr=hati-hatj+lamda(2hati+hatk) and vecr=2hati-hatj+mu(hati+hatj-hatk)

Find the shortest distance between the lines vecr=6hati+2hatj+2hatk+lamda(hati-2hatj+2hatk) and vecr=-4hati+hatk+mu(3hati-2hatj-hatk) .

Find the angle between the lines vecr=2hati+3hatj-4hatk+lambda(2hati+1hatj+2hatk) and vecr=2hati-5hatk+mu(6hati+3hatj+2hatk)

Find the shortest distance between the lines: vecr=6hati+2hatj+2hatk+lambda(hati-2hatj+2hatk) and vecr=-4hati-hatk+mu(3hati-2hatj-2hatk) .

Find the angles between each of the following pairs of lines: vecr=4hati-hatj+lambda(hati+2hatj-hatk) and vecr=hati-hatj+2hatk-mu(2hati+4hatj-4hatk)

Find the shortest distance (S.D.) between the lines : vecr=hatj+lamda(3hati+hatj-2hatk) and vecr=2hati+3hatj-hatk+mu(2hati-hatj+4hatk)

Find the vector and cartesian equations of the plane containing the lines: vecr=hati+2hatj-4hatk+lambda(2hati+3hatj+6hatk) and vecr=3hati+3hatj-5hatk+mu(-2hati+3hatj+8hatk) .

PRADEEP PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXERCISE
  1. Find the equation of the line passing through (1,2,3) and parallel to ...

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  2. Find the equation of the plane, which contains two lines: (x-4)/1=(y-3...

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  3. Find the equation of the plane containingg the lines: vecr=hati+hatj+l...

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  4. Find the vector equation of the line (x-1)/2=(y-2)/-3=(z+3)/4.

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  5. Find the co-ordinates of the points where the line through the points ...

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  6. Find the co-ordinates of the point P, where the line through A(3,-4,-5...

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  7. Find the co-ordinates of the points where the line through the points ...

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  8. Find the distance of the point (-1 , -5 , -10) from the point of inter...

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  9. Show that the lines (x+1)/-3=(y-3)/2=(z+2)/1 and x/1=(y-7)/-3=(z+7)/2 ...

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

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

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

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

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

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

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

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

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

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

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