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NCERT Solutions for Class 11 Math Ch-11: Introduction to Three Dimensional Geometry
NCERT Solutions for Class 11 Maths Chapter 11 Introduction to Three Dimensional Geometry covers the coordinate system in three-dimensional space, the distance formula, and the section formula for points in 3D.
Overview of Topics & Subtopics
Important Questions and Answers
Q1: How many coordinate planes and octants are there in three-dimensional space?
Answer: In three-dimensional space, there are three coordinate planes (the XY-plane, YZ-plane, and ZX-plane), and these three planes divide the space into eight octants.
Q2: What is the distance formula between two points (x1, y1, z1) and (x2, y2, z2) in three-dimensional space?
Answer: The distance between two points in 3D space is given by d = √[(x2 − x1)² + (y2 − y1)² + (z2 − z1)²].
Q3: What is the section formula for finding the coordinates of a point dividing a line segment internally in the ratio m:n?
Answer: If a point P divides the line segment joining (x1, y1, z1) and (x2, y2, z2) internally in the ratio m:n, its coordinates are given by [(mx2 + nx1)/(m+n), (my2 + ny1)/(m+n), (mz2 + nz1)/(m+n)].
Q4: What are the coordinates of the midpoint of a line segment joining two points in 3D space?
Answer: The coordinates of the midpoint of the segment joining (x1, y1, z1) and (x2, y2, z2) are given by [(x1+x2)/2, (y1+y2)/2, (z1+z2)/2], which is a special case of the section formula where the ratio m:n is 1:1.
Q5: What are the coordinates of any point lying on the x-axis in three-dimensional space?
Answer: Any point lying on the x-axis in three-dimensional space has coordinates of the form (x, 0, 0), since both its y-coordinate and z-coordinate must be zero.
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