Chapter 12 : Introduction to Three Dimensional Geometry
Q. A point is on the x-axis. What are its y-coordinate and z-coordinates?
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Q. If a point is in the XZ-plane. What can you say about its y-coordinate?
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Q. Fill in the blanks:
(i) The x-axis and y-axis taken together determine a plane known as______
(ii) The coordinates of points in the XY-plane are of the form_____
(iii) Coordinate planes divide the space into_____ octants
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Q. Name the octants in which the following points lie:
(1, 2, 3), (4, 2, 3)(4, 2, 5), (4, 2, 5), (4, 2, 5), (4, 2, 5), (3, 1, 6), (2, 4, 7)
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Q. Verify the following
(i) (0, 7, 10), (1, 6, 6) and (4, 9, 6) are the vertices of an isosceles triangle
(ii) (0, 7, 10), (1, 6, 6) and (4, 9, 6) are the vertices of a right angled triangle
(iii) (1, 2, 1), (1, 2, 5), (4, 7, 8) and (2, 3, 4) are the vertices of a parallelogram
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Q. Find the equation of the set of points P, the sum of whose distances from A(4, 0, 0) and B(4, 0, 0) is equal to 10.
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Q. Find the distance between the following pairs of points:
(i) (2, 3, 5) and (4, 3, 1)
(ii)(3, 7, 2)and ((2, 4, 1)
(iii) (1, 3, 4) and (1, 3, 4)
(iv) (2, 1, 3) and (2, 1, 3)
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Q. Find the equation of the set of points which are equidistant from the points (1, 2, 3) and (3, 2, 1)
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Q. Show that the points (2, 3, 5), (1, 2, 3) and (7, 0, 1) are collinear.
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Q. Using section formula show that the points A (2, 3, 4), B (1, 2, 1) and C(0, 13, 2) are collinear.
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Q. Find the ratio in which the YZ-plane divides the line segment formed by joining the points (2, 4, 7) and (3, 5, 8)
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Q. Find the coordinates of the points which trisect the line segment joining the points P(4, 2, 6) and Q(10, 16, 6)
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Q. Find the coordinates of the point which divides the line segment joining the points (2, 3, 5) and (1, 4, 6) in the ratio
(i) 2:3 internally
(ii) 2:3 externally
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Q. Given that P(3, 2, 4), Q(5, 4, 6) and R(9, 8, 10) are collinear. Find the ratio in which Q divides PR.
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Q. Find the lengths of the medians of the triangle with vertices A(0, 0, 6), B(0, 4, 0) and (6, 0, 0).
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Q. A point R with x-coordinate 4 lies on the line segment joining the points P(2, 3, 4) and Q(8, 0, 10). Find the coordinates of the point R.
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Q. Three vertices of a parallelogram ABCD are A(3, 1, 2), B(1, 2, 4) and C(1, 1, 2). Find the coordinates of the fourth vertex.
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Q. If the origin is the centroid of the triangle PQR with vertices P(2a, 2, 6), Q(4, 3b, 10) and R(8, 14, 2c), then find the values of a, b and c
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Q. Find the coordinates of a point on y-axis which are at a distance of 52 from the point P(3, 2, 5)
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Q. If A and B be the points (3, 4, 5) and (1, 3, 7) respectively. Find the equation of the set of points P such that PA2 +PB2 =K2, where K is a constant
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