Chapter 11 Introduction To Three Dimensional Geometry EXERCISE 11.1
EXERCISE 11.1
1. A point is on the $x$-axis. What are its $y$-coordinate and $z$-coordinates?
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Answer :
If a point is on the $x$-axis, then its $y$-coordinates and $z$-coordinates are zero.
2. A point is in the $XZ$-plane. What can you say about its $y$-coordinate?
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Answer :
If a point is in the $XZ$ plane, then its $y$-coordinate is zero.
3. Name the octants in which the following points lie:
$ \begin{aligned} & (1,2,3),(4,-2,3),(4,-2,-5),(4,2,-5),(-4,2,-5),(-4,2,5),(-3,-1,6)(-2,-4,-7) . \end{aligned} $
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Answer :
The $x$-coordinate, $y$-coordinate, and $z$-coordinate of point $(1,2,3)$ are all positive. Therefore, this point lies in octant $\mathbf{I}$.
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 $IV.$
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 $VIII.$
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 $\mathbf{V}$.
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 $VI.$
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 $II.$
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 $III.$
The $x$-coordinate, $y$-coordinate, and $z$-coordinate of point $(2,-4,-7)$ are positive, negative, and negative respectively. Therefore, this point lies in octant $VIII.$
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.
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Answer :
(i) $XY-$ plane
(ii) $(x, y, 0)$
(iii) $\text{ Eight }$
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