Introduction to Three Dimensional Geometry MATHS - Introduction to Three Dimensional Geometry

XOZ plane divides the join of (2, 3, 1) and (6, 7, 1) in the ratio:

The ratio in which the line joining the points (1, 2, 3) and (-3, 4, -5) is divided by the xy-plane is:

The image of the point P(1,3,4) in the plane 2x - y + z = 0 is:

The cartesian equation of the line is 3x + 1 = 6y - 2 = 1 - z then its direction ratio are:

What is the length of foot of perpendicular drawn from the point P(3, 4, 5) on y-axis:

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A line is parallel to x-axis if all the points on the line have equal ________.

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If the mid-points of the sides of a triangle AB; BC; CA are D(1, 2, -3), E(3, 0, 1) and F(-1, 1, -4), then the centriod of the triangle ABC is ________.

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The three axes OX, OY, OZ determine ________.

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The coordinates of a point are the perpendicular distance from the ________ on the respectives axes.

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Coordinate planes divide the space into ______ octants.

Find the distance between (2, -1, 3) and (-2, 1, 3) pairs of points.

Find the distance between (-1, 3, -4) and  (1, -3, 4) pairs of points.

Find the distance between (-3, 7, 2) and (2, 4, -1) pairs of points.

Find the distance between (2, 3, 5) and (4, 3, 1) pairs of points.

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)

If the origin is the centriod 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.

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.

Find the equation of the set of points which are equidistance from the points (1, 2, 3) and (3, 2, -1).

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.

Find the length of the medians of the triangle with vertices A (0, 0, 6), B (0, 4, 0) and C (6, 0, 0).

Find the equation of the set of the point P, the sum of whose distance from A(4, 0, 0) and B(-4, 0, 0) is equal to 10.

Find the equation of the set of points P such that PA² + PB² =2k², where A and B are the points (3, 4, 5) and (-1, 3, -7), respectively.

Are the points A(3, 6, 9), B(10, 20, 30) and C(25, -41, 5), the vertices of a right-angled triangle?

Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The points A(1, -1, 3), B(2, -4, 5) and C(5, -13, 11) are collinear.
Reason: If AB + BC = AC, then A, B, C are collinear.

1. Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
2. Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
3. Assertion is correct statement but Reason is wrong statement.
4. Assertion is wrong statement but Reason is correct statement.

Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The foot of perpendicular drawn from the point A(1, 2, 8) on the xy - plane is (1, 2, 0).
Reason: Equation of xy - plane is y = 0.

1. Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
2. Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
3. Assertion is correct statement but Reason is wrong statement.
4. Assertion is wrong statement but Reason is correct statement.