Your Progress 0 / 25 attempted
Q 01 / 25
In three dimensional geometry, the position of a point is completely determined by three real numbers.
Q 02 / 25
The coordinate axes in three dimensional geometry are pairwise perpendicular to each other.
Q 03 / 25
The ordered triples \((2, -1, 3)\) and \((-1, 2, 3)\) represent the same point in space.
Q 04 / 25
If the \(z\)-coordinate of a point is zero, the point lies in the \(xy\)-plane.
Q 05 / 25
The point \((0, 0, 0)\) is called the origin of the three dimensional coordinate system.
Q 06 / 25
All points with coordinates of the form \((x, 0, 0)\) lie on the \(x\)-axis.
Q 07 / 25
The distance between two points in space depends only on their projections on the \(xy\)-plane.
Q 08 / 25
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 09 / 25
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 / 25
The midpoint of the line segment joining two points in space is obtained by averaging only their \(x\)-coordinates.
Q 11 / 25
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 / 25
The coordinates of the centroid of a triangle in space are obtained by averaging the coordinates of its three vertices.
Q 13 / 25
If three points in space are collinear, the area of the triangle formed by them is zero.
Q 14 / 25
Two distinct points always determine a unique plane in space.
Q 15 / 25
The coordinates of a point are independent of the choice of origin.
Q 16 / 25
The distance formula in three dimensions reduces to the two dimensional distance formula when the \(z\)-coordinates of both points are equal.
Q 17 / 25
The locus of points equidistant from two fixed points in space is always a plane.
Q 18 / 25
The midpoint of the segment joining \((a, b, c)\) and \((-a, -b, -c)\) is the origin.
Q 19 / 25
The points \((1,2,3)\), \((2,4,6)\), and \((3,6,9)\) are non-collinear.
Q 20 / 25
The distance between the origin and the point \((x, y, z)\) is \(\sqrt{x^2+y^2+z^2}\).
Q 21 / 25
If three points have the same \(z\)-coordinate, they necessarily lie in a plane parallel to the \(xy\)-plane.
Q 22 / 25
The section formula can be applied only when a point divides a line segment internally.
Q 23 / 25
The distance between two points in space is invariant under translation of the coordinate axes.
Q 24 / 25
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 / 25
The centroid of four non-coplanar points in space always lies inside the tetrahedron formed by them.
Share this Chapter

Found this helpful? Share this chapter with your friends and classmates.

WhatsApp Telegram X / Twitter Facebook LinkedIn

💡 Exam Tip: Share helpful notes with your study group. Teaching others is one of the fastest ways to reinforce your own understanding.

;
📰 Recent Posts

    INTRODUCTION TO THREE DIMENSIONAL GEOMETRY – Learning Resources

    Detailed Notes
    Practice MCQs
    NCERT Solutions
    Practice Advance MCQs

    Get in Touch

    Let's Connect

    Questions, feedback, or suggestions?
    We'd love to hear from you.