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Show that plane ax+by+cz+d=0 divides the...

Show that plane `ax+by+cz+d=0` divides the line segment joining `(x_1,y_1,z_1) and (x_2,y_2,z_2)` in a ratio `-(ax_1+by_1+cz_1+d)/(ax_2+by_2+cz_2+d)`

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MBD PUBLICATION-THREE DIMENSIONAL GEOMETRY-QUESTION BANK
  1. Prove that the line joining (1,2,3),(2,1,-1) intersects the line joini...

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  2. Show that the point (-frac{1}{2},2,0) is the circumcentre of the trian...

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  3. Show that plane ax+by+cz+d=0 divides the line segment joining (x1,y1,z...

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  4. A variable plane is at a constant distance p from the origin and meets...

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  5. A variable plane passes through a fixed point (a,b,c) and meets the co...

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  6. The plane 4x+7y+4z+81=0 is rotated through a right angle about its lin...

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  7. The plane lx+my=0 is rotated about its line of intersection with the p...

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  8. State which of the following statements are true (T) or false(F) The...

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  9. State which of the following statements are true (T) or false(F) The...

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  10. State which of the following statements are true (T) or false(F) The...

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  11. State which of the following statements are true (T) or false(F) The...

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  12. State which of the following statements are true (T) or false(F) The...

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  13. The line (x+2)/(-4)+(y-1)/5=(z-1)/3 and (1-x)/(-4)=(y-0)/5=(2-z)/3 are

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  14. The line passing through (-1,0,1) and perpendicular to the plane x+2y+...

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  15. The line (x+1)/2=(y-6)/1=(z-4)/0 is

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  16. If the line (x-3)/2=(y+k)/(-1)=(z+1)/(-5) lies on the plane 2x-y+z-7 =...

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  17. If l,m,n be d.cs, of a line ,then the line is perpendicular to the pla...

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  18. Find the equation of lines joining the points. (4,-6,1) and (0,3,-1)

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  19. Find the equation of lines joining the points. (a,a,a) and (a,0,a)

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  20. Find the equation of lines joining the points. (2,1,3) and (4,-2,5).

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