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Introduction To Three Dimensional Geometry

Short Answer Type

111.

Find the co-ordinates of a point on y-axis which is at distance of $5 square root of 2$ units from point P(3, -2, 5).

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112. Find the ratio in which the line joining points A (4, 8, 10) and B (6, 10, -8) is divided by the YZ-plane.

Solution not provided.
Ans. 2 : 3 external

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113. Find the locus of point which moves so Uiat its distance from YZ-plane is twice its distance from ZX-plane.

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114. A (1, 2, -1) and B (0, -3, 4) are two points. Find the locus of a point P so that PA² - PB² = 27.

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115. The mid-point of three sides BC, CA and AB of a triangle ABC are D (1, 5, -1), E (6, 4, - 7) and F (2, 3, 4) respectively. Find the lengths of side BC, CA and AB respectively.

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Long Answer Type

116. Find the ratio in which the line joining points A (2, 2, - 3) and B (1, -1, 2) is divided by the XY-plane. Also, find the co-ordinates of the point of intersection.

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Short Answer Type

117. Three vertices of a parallelogram taken in order are A (5, 3, -2), B (1, 2, -3) and C (- 1, -5, 6). Find the co-ordinates of the fourth vertex D.

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Long Answer Type

118.

Show that point A (5, 4, 2), B (-1, -2, 4) and $straight C space open parentheses 13 over 5 comma space 8 over 5 comma space 14 over 5 close parentheses$ are collinear. Find also the ratio in which C divides the join of A and B.

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Short Answer Type

119. The centroid of a triangle whose vertices are A (x, 1, 3), B (-2, y, -5) and C (4, 7, z) is at point G (1, -1, 2). Find values of x, y, z.

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120. Point P (-3, -14, 19) divides the line segment joining points A and B externally in ratio 2 : 3. If the co-ordinates of A are (1, -2, 3), find the co-ordinates of B.

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