## Chapter 28 – Introduction to 3-D coordinate geometry Exercise Ex. 28.1

Name the octants in which the following points lie:

(i) (5, 2, 3)

All are positive, so octant is XOYZ

Name the octants in which the following points lie:

(ii)

(-5, 4, 3)

X is negative and rest are

positive, so octant is X^{‘}OYZ

Name the octants in which the following points lie:

(4,

-3, 5)

Y is negative and rest are

positive, so octant is XOY^{‘}Z

Name the octants in which the following points lie:

(7,

4, -3)

Z is negative and rest are

positive, so octant is XOYZ^{‘}

Name the octants in which the following points lie:

(-5,

-4, 7)

X and Y are negative and Z

is positive, so octant is X’OY’Z

Name the octants in which the following points lie:

(-5,

-3, -2)

All are negative, so

octant is X^{‘}OY^{‘}Z^{‘}

Name the octants in which the following points lie:

(2,

-5, -7)

Y and Z are negative, so

octant is XOY^{‘}Z^{‘}

Name the octants in which the following points lie:

(-7,

2, -5)

X and Z are negative, so

octant is X^{‘}OYZ^{‘}

Find the image of :

(-2, 3, 4) in the yz-plane

YZ plane is x-axis, so

sign of x will be changed. So answer is (2, 3, 4)

Find the image of :

(-5, 4, -3) in the xz-plane.

XZ plane is y-axis, so

sign of y will be changed. So answer is (-5, -4, -3)

Find the image of :

(5, 2, -7) in the xy-plane

XY-plane is z-axis, so

sign of Z will change. So answer is (5, 2, 7)

Find the image of :

(-5, 0, 3) in the xz-plane

XZ plane is y-axis, so

sign of Y will change, So answer is (-5, 0, 3)

Find the image of :

(-4, 0, 0) in the xy-plane

XY plane is Z-axis, so

sign of Z will change So answer is (-4, 0, 0)

A

cube of side 5 has one vertex at the point (1, 0, -1), and the three edges

from this vertex are, respectively, parallel to the negative x and y axes and

positive z-axis. Find the value coordinates of the other vertices of the

cube.

Vertices of cube are

(1, 0, -1) (1, 0, 4) (1,

-5, -1)

(1, -5, 4) (-4, 0, -1)

(-4, -5, -4)

(-4, -5, -1) (4, 0, 4) (1,

0, 4)

Planes

are drawn parallel to the coordinate planes through the points (3, 0, -1) and

(-2, 5, 4). Find the lengths of the edges of the parallelepiped so formed.

3-(-2)=5, |0-5|=5,

|-1-4|=5

5, 5, 5 are lengths of

edges

Planes

are drawn through the points (5, 0, 2) and (3, -2, 5) parallel to the

coordinate planes. Find the lengths of the edges of the rectangular

parallelepiped so formed.

5-3=2, 0-(-2)=2, 5-2=3

2, 2, 3 are lengths of

edges

Find

the distances of the point p(-4, 3, 5) from the

coordinate axes.

The

coordinate of a point are (3, -2, 5). Write down the

coordinates of seven points such that the absolute values of their

coordinates are the same as those of the coordinates of the given point.

(-3, -2, -5) (-3, -2, 5)

(3, -2, -5) (-3, 2, -5) (3, 2, 5)

(3, 2, -5) (-3, 2, 5)

## Chapter 28 – Introduction to 3-D coordinate geometry Exercise Ex. 28.2

Verify the following

(5, -1, 1), (7, -4, 7), (1, -6, 10) and (-1, -3, 4) are

the vertices of a rhombus.

Find the equation of the set of the points P such that its distances from the points A(3, 4, -5) and B(-2, 1, 4) are equal.

## Chapter 28 – Introduction to 3-D coordinate geometry Exercise Ex. 28.3

The

vertices of the triangle are A(5, 4, 6), B(1, -1, 3)

and C(4, 3, 2). The internal bisector of angle A meets BC at D. Find the

coordinates of D and the Length AD.

A

point C with z-coordinate 8 lies on the line segment joining the points A(2, -3, 4) and B(8, 0, 10). Find its coordinates.

Show

that three points A(2, 3, 4), B(-1, 2, -3) and C(-4, 1, -10) are collinear

and find the ratio in which C divides AB.

Find

the ratio in which the line joining (2, 4, 5) and (3, 5, 4) is divided by the

yz-plane.

Find the ratio in which the line segment joining the

points (2, -1, 3) and (-1, 2, 1) is divided by the plane

x+ y +

z = 5.

If

the points A(3, 2, -4), B(9, 8, -10) and C(5, 4, -6) are collinear, find the

ratio in which C divides AB.

The

mid-points of the sides of a triangle ABC are given by (-2, 3, 5), (4, -1, 7) and (6, 5, 3). Find the coordinates of A, B and C.

A(1, 2, 3),

B(0, 4, 1), C(-1, -1, -3) are the vertices of a triangle ABC. Find the point

in which the bisector of the angle meets BC.

Find

the ratio in which the sphere x^{2}+y^{2 }+z^{2} =

504 divides the line joining the points (12, -4, 8) and (27, -9, 18).

Show that the plane ax + by + cz

+ d = 0 divides the line joining the points (x_{1},y_{1},z_{1})

and (x_{2},y_{2},z_{2})

in the ratio –

Find

the centroid of a triangle, mid-points of whose

sides are (1, 2, -3), (3, 0, 1) and (-1, 1, -4).

The centroid of a triangle ABC is at the point (1, 1, 1). If the coordinate of A and B are (3, -5, 7) and (-1,

7, -6) respectively, find the coordinates of the point C.

Find

the coordinates of the points which tisect the line

segment joining the points P(4, 2, -6) and Q(10,

-16, 6).

Using

section formula, show that the points A(2, -3, 4),

B(-1, 2, 1) and C(0, 1/3, 2) are collinear.

Given

that P(3, 2, -4), Q(5, 4, -6) and R(9, 8, -10) are

collinear. Find the ratio in which Q divides PR.

Find

the ratio in which the line segment joining the points (4, 8, 10) and (6, 10, -8) is divided by the yz-plane.