Referring to the AP Inter 1st Year Maths Study Material Chapter 11 Introduction to 3D Geometry Exercise 11a Solutions makes it easier to understand complex problems.
AP Inter 1st Year Maths Introduction to 3D Geometry Solutions Exercise 11a
Question 1.
A point is on the X-axis. What are its y-coordinates and Z-coordinates.
Solution:
If a point is on the X-axis, then its y-coordinate and z-coordinates are zero.
Question 2.
A point is in the XZ-Plane. What can you say about its y-coordinate?
Solution:
If a point is in the XZ plane, then its y-coordinate is zero.
Question 3.
Name the octants in which the following points lie (1, 2, ), (4, -2, 3), (4, -2,-5), (4, 2, -5) (-4, 2, -5), (-4, 2, 5), (-3, -1, 6), (-2, -4, -7).
Solution:
1) The x-coordinate, y-coordinate and z-coordinate of point (1, 2, 3) are all positive. Therefore, this point lies in octant I. i.e. (1, 2, 3) → I
2) The x-coordinate, y-coordinate and z-coordinate of point (4, -2, 3) are positive, negative and positive respectively. Therefore, this point lies in octant IV.
i. e., (4, -2, 3) → IV
3) The x-coordinate, y-coordinate and z-coordinate of point (4, -2, -5) are positive, negative and negative respectively. Therefore, this point lies in octant VIII.
i. e., (4, -2, -5) → VIII
4) The x-coordinate, y-coordinate and z-coordinate of point (4, 2, -5) are positive, positive and negative respectively. Therefore, this point lies in octant V.
i.e., (4, 2, -5) → V
5) The x-coordinate, y-coordinate and z-coordinate of point (-4, 2, -5) are negative, positive and negative respectively. Therefore, this point lies in octant VI.
i.e., (-4, 2, -5) → VI
6) The x-coordinate, y-coordinate and z-coordinate of point (-4, 2, 5) are negative, positive and positive respectively. Therefore, this point lies in octant II.
i.e., (-4, 2, 5) → II
7) The x-coordinate, y-coordinate and z-coordinate of point (-3, -1, 6) are negative, negative and positive respectively. Therefore, this point lies in octant III.
i.e., (-3, -1, 6) → III
8) The x-coordinate, y-coordinate and z-coordinate of point (-2, -4, -7) are all negative. Therefore, this point lies in octant VII.
i.e., (-2, -4, -7) → VII
Question 4.
Fill in the Blanks.
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 octants.
Solution:
i) The X-axis 8s Y-axis taken together determine a plane known as XY-plane.
ii) The coordinates of points in the xy-plane are of the form (x, y, 0).
iii) Coordinate planes divide the space into eight octants.
Question 5.
i) The point (x, 0, 0) lies on _________ axis.
ii) The point (0, y, 0) lies on _________ axis.
iii) The point (0, 0, z) lies on _________ axis.
iv) The point (x, y, 0) lies on _________ plane.
v) The point (x, 0, z) lies on _________ plane.
Solution:
i) X-axis
ii) Y-axis
iii) Z-axis
iv) XY-plane
v) ZX-plane