Introduction to 3D coordinate geometry - Gujarat Board (GSEB) STD 11 Science MATHS Questions

Q 1(Each question 1 marks)1 Mark

Find the point on x-axis which is equidistant from the points A(3, 2, 2) and B(5, 5, 4).

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Q 2(Each question 1 marks)1 Mark

Write the length of the perpendicular drawn from the point P(3, 5, 12) on x-axis

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Q 3(Each question 1 marks)1 Mark

Find the image of: (-5, 0, 3) in the xz-plane.

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Q 4(Each question 1 marks)1 Mark

Name the octants in which the following points lie: (-7, 2, -5)

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Q 5(Each question 1 marks)1 Mark

Write the coordinates of third vertex of a triangle having centroid at the origin and two vertices at (3, -5, 7) and (3, 0, 1).

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Q 6(Each question 2 marks)2 Marks

Using section formula, show that the points A(2, -3, 4), B(-1, 2, 1) and $\text{C}\Big(0, \frac{1}{3}, 2\Big)$ are collinear.

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Q 7(Each question 2 marks)2 Marks

Find the coordinates of the points which tisect the line segment joining the points P(4, 2, -6) and Q(10, -16, 6).

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Q 8(Each question 2 marks)2 Marks

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 9(Each question 2 marks)2 Marks

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

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Q 10(Each question 2 marks)2 Marks

Find the distance between the points P and Q having coordinates (-2, 3, 1) and (2, 1, 2).

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Q 11(Each question 3 marks)3 Marks

Find the ratio in which the line Segment joining the points (2, -1, 3) and (-1, 2, 1) is divided by the plane x + y + z =5.

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Q 12(Each question 3 marks)3 Marks

Planes are drawn parallel to the coordinate planes through the points (3, 0, -1) and (-2, 5, 4). Find the lengths of the edges of the parallelopiped so formed.

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Q 13(Each question 3 marks)3 Marks

Find the ratio in which the sphere $x^2 + y^2 + z^2 = 504$ divides the line joining the points $(12, -4, 8)$ and $(21, -9, 18)$.

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Q 14(Each question 3 marks)3 Marks

A(1, 2, 3), B(0, 4, 1), C(-1, -1, -3) are the vertices of a triangle ABC. Find the point in which the bisector of the angle $\angle\text{BAC}$ meets BC.

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Q 15(Each question 3 marks)3 Marks

The centroid of a triangle ABC is at the point (1, 1, 1). If the coordinates of A and B are (3, -5, 7) and (-1, 7, -6) respectively, find the coordinates of the point C.

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Q 16(Each question 4 marks)4 Marks

Show that the points (a, b, c), (b, c, a) and (c, a, b) are the vertices of an equilateral triangle.

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Q 17(Each question 4 marks)4 Marks

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

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Q 18(Each question 4 marks)4 Marks

Show that the points (0, 7, 10), (-1, 6, 6) and (-4, 9, 6) are the vertices of an isosceles right-angled triangle.

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Q 19(Each question 4 marks)4 Marks

Using distance formula prove that the following points are collinear: P(0, 7, -7), Q(1, 4, -5) and R(-1, 10, -9)

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Q 20(Each question 4 marks)4 Marks

Find the coordinates of the point which is equidistant from the four points $O(0, 0, 0), A(2, 0, 0), B(0, 3, 0)$ and $C(0, 0, 8)$.

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Introduction to 3D coordinate geometry question types

Introduction to 3D coordinate geometry questions

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Introduction to 3D coordinate geometry MATHS - Introduction to 3D coordinate geometry

Introduction to 3D coordinate geometry question types

Introduction to 3D coordinate geometry questions

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