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Show that the points (1, 2, 3), (2, 3, 1...

Show that the points (1, 2, 3), (2, 3, 1) and (3, 2, 1) form an equilateral triangle.

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Show that the points (2, 3, 5), (-1, 5, -1) and (4, -3, 2) form a right angled isosceles triangle.

Show that the points (2,4),(2,6) (2+sqrt3,5) form an equilateral triangle.

I : The points (-2,3,5 ), (1,,2,3 ),(7,0,-1 ) are collinear. II: The points (2 ,-1,1 ) (1-3-5 ), (3,-4,-4 ) form an equilateral triangle.

Show that the points A(-1, -2), B(4, 3), C(2, 5) and D(- 3, 0) in that order form a rectangle.

Show that the points (0, -1, 0), (2,1,-1), (1,1,1), (3,3,0) are coplanar.

Show that the points (1,3),(3,-1),(-5,-5) form a right angled triangle.

If H, G, S and I respectively denote orthocentre, centroid, circumcentre and in-centre of a triangle formed by the points (1, 2, 3), (2, 3, 1) and (3, 1, 2), then find H, G, S, I

AAKASH SERIES-3D-COORDINATE SYSTEM-EXERCISE - 5 (SHORT ANSWER QUESTIONS)
  1. Show that the point A(-4, 9, 6), B(-1,6,6), C(0,7,10) form a right ang...

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  2. Show that the points (1, 2, 3), (2, 3, 1) and (3, 2, 1) form an equila...

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  3. Show that ABCD is a square where A,B,C,D are the points (0,4,1),(2,3,-...

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  4. Show that the points (5,-1,-1),(-1,5,-1)(-1,-1,5),(-3,-3,-3) are the v...

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

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  6. Show that the points A=(1,2,3),B=(7,0,1), C=(-2,3,4) are colinear.

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  7. S.T The points are collinear (ii) A(3,-2,4), B(1,1,1),C(-1,4,-2)

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  8. Show that the points A(3,2,-4),B(5,4,-6) andC(9,8,-10) are collinear a...

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  9. Show that the points O(0,0,0), A(2,-3,3) B(-2,3,-3) are collinear. Fin...

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  10. For what value of t, the points (2,-1,3),(3,-5,t) and (-1,11,9) are co...

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  11. A(5,4,6), B(1,-1,3),C(4,3,2) are three points. Find the coordinates of...

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  12. A(3,2,0), B(5,3,2), C(-9,6,-3) are vertices of a triangle. bar(AD), th...

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  13. Show that the point whose distance from Y-axis in thrice its distance ...

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  14. P is a variable point which moves such that 3PA =2PB. If A(-2,2,3) and...

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  15. The ends of the hypotenuse of a right angled triangle are (2,0,-3) ,(0...

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  16. A,B,C are three points OX,OY,OZ respectively, at distance a,b,c from t...

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  17. If A(4,8,12), B(2,4,6), C(3,5,4) and D(5,8,5) are four points, show t...

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  18. Find the point of intersectoon of the lines vec(AB) and vec(CD) where ...

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  19. The incentre of the triangle formed by (0,0,0),(3,0,0),(0,4,0) is

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  20. If the point (1, 2, 3) is changed to the point (2, 3, 1) through trans...

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