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Find the equations of two planes through the point `(4,2,1),(2,1,-1)` and making angles `pi/4` with the plane `x-4y+z=9.`

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PRADEEP PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXERCISE
  1. The distance of the point (2,1,-1) from the plane x-2y+4z=9 is :

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  2. Find the distance between the point (7,2,4) and the plane determined b...

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  3. Find the equations of two planes through the point (4,2,1),(2,1,-1) an...

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  4. Find the length of the projection of the line segment joining the poin...

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  5. Show that the line L whose vector equation is vecr=2hati-2hatj+3hatk+l...

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  6. Find the equation of plane passing through the point (1,4,-2) and para...

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  7. Find the equation of the planes parallel to the plane x-2y+2z-3=0 and ...

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  8. The planes 2x-2y+4z+5=0 and 3x-3y+6z-1=0 are

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  9. Find the distance between the parallel planes 2x-y+3z+4=0 and 6x-3y+9z...

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  10. Show that the equation of the plane through the line x/l=y/m=z/n and p...

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  11. Two systems of rectangular axes have the same origin. If a plane cuts ...

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  12. Show that the points P(hati-hatj+3hatk) and Q(3hati+3hatj+3hatk) are e...

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  13. Find in parametric form, the equations of the line x+y+z+1=0, 4x+y-2z+...

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

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  15. Find the equation of the plane containing the line of intersection of ...

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  16. Find the vector quation of the plane containing the line of intersecti...

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  17. Find the equation of the plane which is perpendicular to the plane 5 x...

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  18. Find the equation of the plane bisectiing the angles between the plane...

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  19. Show that the lines (x+4)/3=(y+6)/5=(z-1)/-2 and 3x-2y+z+5=0=2x+3y+4z-...

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  20. Prove that the line of section of the planes 5x+2y-4z+2=0 and 2x+8y+2z...

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