Prove that the points ( - 1 , - 3, 4) ...

Prove that the points ( - 1 , - 3, 4) , ( 1 , - 6, 10) , ( 7 , - 4 , 7 ) and ( 5 , - 1 , 1) are the vertices of the rhombus .

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Prove that the points ( 2 , 3, 5) , ( - 4 , 7 , - 7) , ( - 2 , 1 , -10) and ( 4 , - 3 , 2) are the vertices of a rectangle .

Prove that the points A(-5 , 1 , 1) , B(1 , 3 , 4) , C ( - 1 , 6 , 10) and D (-7 , 4, 7) taken in order are the vertices of a rhombus .

Prove that the points ( 4 , 7 , 6) , ( 2 , 3 , 2 ) , ( - 1, -2, -1) and ( 1, 2 , 3) taken in order are the vertices of a parallelogram . Is the the parallelogram a rectangle?

By vector method, show that the four points (7, 2, -3), (6, 1, 4), (-3, -4, -1) and (-2, -3, -8) are the vertices of a parallelogram.

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 that the points A (4 , 7 , -6) , B (2 , 5 , -4) and C ( 1 , 4 , -3) are collinear.

Prove that the points (2,-2) ,(8,4), (5,7) and (-1,1) are the vertices of a rectangle , find the area of the rectangle.

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

Using direction numbers show that points P(4, 7, 8) and Q(2, 3, 4), R(-1, -2, 1) and S(1, 2, 5) taken in order, are the vertices of a parallelogram. Is the parallelogram a rectangle?

Prove that the points A (-2,-1) , B (5,4) C (6,7) and D (-1,2) are the vertices of a parallelogram.

CHHAYA PUBLICATION-INTRODUCTION TO THREE-DIMENSIONAL COORDINATE GEOMETRY -Very Short Answer Type Questions

Determined the equation to the locus of the point which is equidistant...
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Find the coordinates of the point which is equidistant from the points...
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Find the equation to the locus of the point whose distance from the po...
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Find the perimeter of the triangle whose vertices are ( 0 , 1 , 2) , ...
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Find the images of the point ( 3 , -4 , 6) with respect to yz-...
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Find the images of the point ( 3, - 4 , 6) with respect to zx-plan...
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Find the images of the point (3, - 4 , 6) with respect to xy - pla...
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Prove that the points ( 4 , 7 , 6) , ( 2 , 3 , 2 ) , ( - 1, -2, -1) ...
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Three consecutive vertices of a parallelogram are ( 1 , 2, - 4) , ( -...
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Two vertices of the parallelogram ABCD are A( 8 , 14 , 12) and B( ...
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If (x(1),y(1),z(1)) , (x(2),y(2),z(2)) , (x(3) ,y(3),z(3)) and (x...
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Determine the coordinates of the point which is equiistant from the ...
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Find the distance of the point ( 2 , 4 , 3) from the x-axis and from t...
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Find the equation to the locus of a point the sum of the squares of w...
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Prove that the four points ( 1 , 1 , 1) , (-2 , 4 , 1) , (-1 , 5 ...
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Prove that the points ( 2 , 3, 5) , ( - 4 , 7 , - 7) , ( - 2 , 1 ,...
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Show that the points ( 0 ,0,0) , ( - 2 , 0, 0) , ( 0 , 2 , 0) and...
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Find the coordinates of the points of trisection of the line-segment ...
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Prove that the points ( - 1 , - 3, 4) , ( 1 , - 6, 10) , ( 7 , - ...
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The coordinates of the points A , B , C and D are ( 1 , 1 , 1) , ( -...
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