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Introduction To Three Dimensional Geometry

Short Answer Type

101. Find the ratio in which the line joining A (1, 2, 1) and B (3, 4, - 2) is divided by yz-plane. Also, find the co-ordinates of the point of division.

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102. Find die distance between the point A (- 1, 3, - 4) and the mid-point of the join of the points P(-2, 4, 0) and Q (-4, 6,-4).

Solution not provided.
Ans. $2 square root of 3$

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103.

Find the octant in which following points lie:
(i) (1, 4, -2) (ii) (2, 1, 4) (iii) (-2, -1, 5) (iv) (1, -3, -1) (v) (2, -4, 3)

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Long Answer Type

104.

Write down the co-ordinates of the foot of perpendicular from point P (2, - 3, 4) upon (i) x-axis (ii)y-axis (iii) z-axis.

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105.

Write the co-ordinates of the foot of perpendiculars from point P (2, 4, 5) to (i) the XY-plane (ii) the YZ-plane (iii) the ZX-plane.

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106. Verify that A (-1, -6, 10), B (1, -3, 4), C (- 5, -1, 1) and D (-7, -4, 7) are the vertices of a rhombus.

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Short Answer Type

107.

Using distance formula, show that the following sets of points are collinear.
(i) (-1, 4, -2), (2, -2, 1), (0, 2, -1) (ii) (3, -5, 1), (-1, 0, 8), (7, - 10. - 6).

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108. Using section formula, show that the following sets of points are collinear:
(i) (4, 5, -5), (0, -11, 3), (2, -3, -1) (ii) (-2, 3, 5), (1, 2, 3), (7, 0, -1).

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Long Answer Type

109. Show that A (-2, 6, -2), B (0, 4, -1) and C (-2, 3, 1) are the vertices of an isosceles right angled triangle.

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110. Find the equation of set of points which moves so that its distances from points A (3, 4, - 5) and B (-2, 1, 4) are equal.

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