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

Show that the plane ax+by+ca+d=0 divides the line joining the points `(x_1,y_1,z_1) & (x_2,y_2,z_2)` in the ratio -`(ax_1+by_1+cz_1+d_1)/(ax_2+by_2+cz_2+d_2)`

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PATHFINDER-3D-GEOMETRY-QUESTION BANK
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  3. Prove that the triangle formed by joining the three points whose co-or...

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  4. A,B,C are three points on the axes of x, y and z respectively at dist...

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  5. Find the locus of a point P such that3bar(PA^2)=2bar(PB^2)where A(1,1,...

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  6. Find the possible octants where the point (x,y,z)may lie for z-y=0

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  7. Find the octants which contain the point (x,y,z) satisfying xygt0

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  8. Give the interpretation of the following equation x=0,y=0

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  9. Give the interpretation of the following equation y=0,z=0

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  10. Give the interpretation of the following equation x=a,z=c

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  11. Prove that the points (1,-3,1), (0,1,2), (2,-1,3) are the vertices of ...

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  12. The midpoints of the sides of a triangle are (1,5,-1), (0,4,-2) & (2,3...

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  13. If the origin is the centroid of the triangle PQR with vertices P(2a, ...

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  14. Show that the points (1,1,1), (-2,4,1), (-1,5,5) & (2,2,5) form a squa...

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  15. Find the coordinates of the points which divide the segment joining th...

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  16. A & B are two pts (0,2,3) and (2,-2,1) respectively find the locus of ...

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  17. find the equation of the sphere passing through the four points (0,0,0...

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  18. Find the ratio in which the yz-plane divides the join of the points (-...

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  19. A and B are two points (0,2,3) and (2,-2,1) respectively. Find the loc...

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  20. Show that the plane ax+by+ca+d=0 divides the line joining the points (...

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