Class 11 • Maths • Chapter 11
INTRODUCTION TO THREE DIMENSIONAL GEOMETRY
True & False Quiz
X. Y. Z. Space awaits.
✓True
✗False
25
Questions
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Ch.11
Chapter
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XI
Class
Why True & False for INTRODUCTION TO THREE DIMENSIONAL GEOMETRY?
How this format sharpens your conceptual clarity
🔵 3D Geometry extends coordinate geometry into space — foundation for vectors, solid geometry and computer graphics.
✅ T/F questions test basic but tricky facts about coordinate axes, planes, octants, and the 3D distance formula.
🎯 Common error: a point on the y-axis has coordinates (0,y,0) — NOT (y,0,0).
📋
Read each statement carefully. Click True or False — instant feedback with explanation appears. Submit anytime; unattempted questions are marked Skipped.
Q 1
In three dimensional geometry, the position of a point is completely determined by three real numbers.
Q 2
The coordinate axes in three dimensional geometry are pairwise perpendicular to each other.
Q 3
The ordered triples \((2, -1, 3)\) and \((-1, 2, 3)\) represent the same point in space.
Q 4
If the \(z\)-coordinate of a point is zero, the point lies in the \(xy\)-plane.
Q 5
The point \((0, 0, 0)\) is called the origin of the three dimensional coordinate system.
Q 6
All points with coordinates of the form \((x, 0, 0)\) lie on the \(x\)-axis.
Q 7
The distance between two points in space depends only on their projections on the \(xy\)-plane.
Q 8
The distance between the points \((x_1, y_1, z_1)\) and \((x_2, y_2, z_2)\) is given by \(\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}\).
Q 9
If two points have the same \(x\)- and \(y\)-coordinates but different \(z\)-coordinates, they lie on a line parallel to the \(z\)-axis.
Q 10
The midpoint of the line segment joining two points in space is obtained by averaging only their \(x\)-coordinates.
Q 11
The point dividing the line segment joining \(A(x_1,y_1,z_1)\) and \(B(x_2,y_2,z_2)\) internally in the ratio \(m:n\) has coordinates \(\left(\frac{mx_2+nx_1}{m+n}, \frac{my_2+ny_1}{m+n}, \frac{mz_2+nz_1}{m+n}\right)\).
Q 12
The coordinates of the centroid of a triangle in space are obtained by averaging the coordinates of its three vertices.
Q 13
If three points in space are collinear, the area of the triangle formed by them is zero.
Q 14
Two distinct points always determine a unique plane in space.
Q 15
The coordinates of a point are independent of the choice of origin.
Q 16
The distance formula in three dimensions reduces to the two dimensional distance formula when the \(z\)-coordinates of both points are equal.
Q 17
The locus of points equidistant from two fixed points in space is always a plane.
Q 18
The midpoint of the segment joining \((a, b, c)\) and \((-a, -b, -c)\) is the origin.
Q 19
The points \((1,2,3)\), \((2,4,6)\), and \((3,6,9)\) are non-collinear.
Q 20
The distance between the origin and the point \((x, y, z)\) is \(\sqrt{x^2+y^2+z^2}\).
Q 21
If three points have the same \(z\)-coordinate, they necessarily lie in a plane parallel to the \(xy\)-plane.
Q 22
The section formula can be applied only when a point divides a line segment internally.
Q 23
The distance between two points in space is invariant under translation of the coordinate axes.
Q 24
If the coordinates of three points satisfy a linear relation \(\lambda_1 A + \lambda_2 B + \lambda_3 C = 0\) with \(\lambda_1+\lambda_2+\lambda_3=0\), then the points are collinear.
Q 25
The centroid of four non-coplanar points in space always lies inside the tetrahedron formed by them.
Key Takeaways — INTRODUCTION TO THREE DIMENSIONAL GEOMETRY
Core facts for CBSE Boards & JEE
1
x-axis: (x,0,0); y-axis: (0,y,0); z-axis: (0,0,z).
2
XY-plane: z=0; YZ-plane: x=0; ZX-plane: y=0.
3
Three coordinate planes divide space into 8 octants.
4
Distance = √((x₂−x₁)²+(y₂−y₁)²+(z₂−z₁)²).
5
Midpoint = ((x₁+x₂)/2, (y₁+y₂)/2, (z₁+z₂)/2).
6
Distance from origin to (a,b,c) = √(a²+b²+c²).