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Show that the point A(1, 3, 0), B(–5, 5,, 2), C(–9, –1, 2) and D(–3, –3, 0) are the vertices of a parallelogram ABCD, but it is not a rectangle.

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Show that the points A(3, 5), B(6, 0), C(1, -3) and D(-2, 2) are the vertices of a square ABCD.

Show that the points A(1, 0), B (5, 3), C (2, 7) and D (-2, 4) are the vertices of a rhombus.

Show that the points A (1, 0), B(5, 3), C (2, 7) and D(-2, 4) are the vertices of a rhombus.

Prove that the points A(0, 4, 1), B(2, 3, -1), C(4, 5, 0) and D(2, 6, 2) are vertices of a square.

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Show that the points A" "(1," "2," "3) , B" "(1," "2," "1) , C" "(2," "3," "2) and D" "(4," "7," "6) are the vertices of a parallelogram ABCD, but it is not a rectangle.

CBSE COMPLEMENTARY MATERIAL-INTRODUCTION TO THREE-DIMENSIONAL COORDINATE GEOMETRY-SHORT ANSWER TYPE QUESTIONS
  1. Whhat are the coordinates of the vertices of a cube whose edge is 2 un...

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  2. Let A, B, C be the feet of perpendiculars from point P(1, –2, –3) on t...

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  3. If a parallelopiped is formed by planes drawn through the points ( 5,8...

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  4. The length of the longest piece of a string that can be stetched strai...

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  5. Find the coordinate of the point P which is three-fourth of the way fr...

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  6. Show that points (4, –3, –1), (5, –7, 6) and (3, 1, –8) are collinear.

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  7. Find the point on y-a xi s which is equidistant from the points (3,1,2...

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  8. Determine the point in yz plane which is equidistant from three points...

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  9. The centroid of ∆ABC is at (1, 1, 1). If coordinates of A and B are (3...

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  10. Find the length of the medians of the triangle with vertices A(0, 0, 3...

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  11. If the extremities (end points) of a diagonal of a square are (1,-2,3)...

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  12. Three consecutive vertices of a parallelogram ABCD are A(6,2,4) ,B(2,...

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  13. If the points A(1, 0, –6), B(3, p, q) and C(5, 9, 6) are collinear, fi...

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  14. Show that the point A(1, 3, 0), B(–5, 5,, 2), C(–9, –1, 2) and D(–3, –...

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  15. The mid points of the sides of a triangle are (5, 7, 11), (0, 8, 5) a...

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  16. Find equation of an ellipse having vetices (0, pm5) and foc (0,pm4). F...

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  17. Prove that the points ( 0,-1,-7) , (2,1,-9) and (6,5,-13) are collinea...

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  18. Let A(3, 2, 0), B(5, 3, 2) C(-9, 6, -3) be three points forming atria...

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  19. Describe the vertices and edges of the rectangular parallelepiped with...

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  20. Find the coordinates of the point which is equidistant from the point ...

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