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Title: Introduction To 3D Dimensional Geometry
Description: In this file you will Get notes of introduction To 3 Dimensional Geometry Of Mathematics
Description: In this file you will Get notes of introduction To 3 Dimensional Geometry Of Mathematics
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NCERT Solutions for Class 11 Maths Chapter 12
Introduction to Three Dimensional Geometry Class 11
Chapter 12 Introduction to Three Dimensional Geometry Exercise 12
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1 : Solutions of Questions on Page Number : 271
Q1 :
A point is on the x-axis
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Q2 :
A point is in the XZ-plane
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Q3 :
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)
Answer :
The x-coordinate, y-coordinate, and z-coordinate of point (1, 2, 3) are all positive
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The x-coordinate, y-coordinate, and z-coordinate of point (4, -2, 3) are positive, negative, and positive respectively
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The x-coordinate, y-coordinate, and z-coordinate of point (4, -2, -5) are positive, negative, and negative respectively
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The x-coordinate, y-coordinate, and z-coordinate of point (4, 2, -5) are positive, positive, and negative respectively
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The x-coordinate, y-coordinate, and z-coordinate of point (-4, 2, -5) are negative, positive, and negative respectively
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The x-coordinate, y-coordinate, and z-coordinate of point (-4, 2, 5) are negative, positive, and positive respectively
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The x-coordinate, y-coordinate, and z-coordinate of point (-3, -1, 6) are negative, negative, and positive respectively
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The x-coordinate, y-coordinate, and z-coordinate of point (2, -4, -7) are positive, negative, and negative respectively
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Q4 :
Fill in the blanks:
Answer :
(i) The x-axis and y-axis taken together determine a plane known as
(ii) The coordinates of points in the XY-plane are of the form
(iii) Coordinate planes divide the space into
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octants
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2 : Solutions of Questions on Page Number : 273
Q1 :
Find the distance between the following pairs of points:
(i) (2, 3, 5) and (4, 3, 1) (ii) (-3, 7, 2) and (2, 4, -1)
(iii) (-1, 3, -4) and (1, -3, 4) (iv) (2, -1, 3) and (-2, 1, 3)
Answer :
The distance between points P(x1, y1, z1) and P(x2, y2, z2) is given
by
(i) Distance between points (2, 3, 5) and (4, 3, 1)
(ii) Distance between points (–3, 7, 2) and (2, 4, –1)
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(iii) Distance between points (–1, 3, –4) and (1, –3, 4)
(iv) Distance between points (2, –1, 3) and (–2, 1, 3)
Q2 :
Show that the points (-2, 3, 5), (1, 2, 3) and (7, 0, -1) are collinear
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Points P, Q, and R are collinear if they lie on a line
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Q3 :
Verify the following:
(i) (0, 7, -10), (1, 6, -6) and (4, 9, -6) are the vertices of an isosceles triangle
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(iii) (-1, 2, 1), (1, -2, 5), (4, -7, 8) and (2, -3, 4) are the vertices of a parallelogram
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Here, AB = BC ≠ CA
Thus, the given points are the vertices of an isosceles triangle
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Therefore, by Pythagoras theorem, ABC is a right t
Title: Introduction To 3D Dimensional Geometry
Description: In this file you will Get notes of introduction To 3 Dimensional Geometry Of Mathematics
Description: In this file you will Get notes of introduction To 3 Dimensional Geometry Of Mathematics