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Show that the points (1,1,1), (-2,4,1), ...

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

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Prove that the four ponts (1,1,1),(-2,4,1),(-1,5,5) and (2,2,5) are the vertices of a square.

Show that the points (1, 7), (4, 2), (-1, -1) and (-4, 4) are the vertices of a square .

By using section formula, show that the points .(1, 2, 3), (-2, 4, 2) and (7, -2, 5) are colinear

Show that the points (-2,3,5) ,(1,2,3) and (7,0,-1) are collinear

Show that the points (-2,-1),(5,4),((6,7) and (-1,2) are the vertices of a parallelogram .Is the parallelogram a rectangle ?

Show that the points A=(2,-1,1),B=(1,-3,-5) and C=(3,-4,-4) are vertices of a right angled triangle (using vector method).

Show that the points P(-2,3,5) ,Q (1,2,3) and R (7,0,-1) are collinear

Show that the points (2,1) (0,0) (-1,2) and (1,3) are the vertices of a square.

Show that the points (-4, -7), (-1, 2), (8, 5) and (5, -4) taken in order are the vertices of a rhombus. Find its area. (Hint : Area of rhombus = (1)/(2)xx product of its diagonals)

show by vector method that the points (2, -1, 3), (3, -5, 1) and (-1, 11, 9) are collinear.

PATHFINDER-3D-GEOMETRY-QUESTION BANK
  1. Find the locus of a moving point whose distance from the point(1,-1,2)...

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  2. Find the ratio in which the line joining the pts (-3,4,8) and (5,-6,4)...

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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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