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Prove that the lines frac[x+3][2]=frac[y...

Prove that the lines `frac[x+3][2]=frac[y+5][3]=frac[z-7][-3]` and `frac[x+1][4]=frac[y+1][5]=frac[z+1][-1]` are coplanar. Find the equation of plane containing them.

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Find the equation of the plane passing through the line frac[x+1][-3]=frac[y-3][2]=frac[z+2][1] and the point (0,7,-7). Also show that the line x=frac[7-y][3]=frac[z+7][2] lies in this plane.

MODERN PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXERCISE
  1. Find the equation of the plane passing through the line of intersectio...

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  2. Find the equation of the plane .Passing through the point (2,3-1) and ...

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  3. Bisecting the line segment joining (-1,4,3) and (5,-2,-1) at right ang...

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  4. Find the equation of the plane Paralel to the plane 2x-y+3z+1=0 and at...

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  5. Writing the equation of the plane 3x-2y+z+2=0 in normal form find its ...

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  6. A variable plane moves in such a way that the sum of the reciprocals o...

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  7. In each of the following case, verift whether the four given points ar...

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  8. Find the points of intersection of the line (x-1)/1=(y+2)/ 3 =(z-1)/(...

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  9. Find the angle between the plane x+y+4=0 and the line (x+3)/2=(y-1)/1=...

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  10. If the edges of a rectangular parallelopiped are of lengths a, b, c, t...

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  11. Find the equation of the bisector planes of the angles between the pla...

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  12. A variable plane meets the coordinate axes at P, Q, R points. If the p...

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  13. Find the equation of the straight line perpendicular to the line (x-2)...

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  14. Find the distance of the point (1,-2,3) from the plane x-y+z=5, measur...

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  15. Prove that the lines frac[x+3][2]=frac[y+5][3]=frac[z-7][-3] and frac[...

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  16. Find the equation of the image of the line (x - 1)/2 = (y + 2)=( z - 1...

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  17. Find the shortest distance between the lines  (x-8)/(3) = (y+9)/(-16) ...

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  18. Find the equation of the straight line perpendicular to the line (x-2)...

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  19. Find the distance of the point (-1,-5,-10) from the point of intersect...

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  20. Find the distance of the point (1,-1,-10) from the line (x-4)/1=(y+3)/...

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