## 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?

## Show Answer

**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} $

## Show Answer

**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.

## Show Answer

**Answer :**

(i) $XY-$ plane

(ii) ${(x, y, 0)}$.

(iii) ${\text{ eight }}$