OP Malhotra Class-11 **Coordinates in 3-Dimensions** S.Chand ISC Maths Solution Chapter-26. Step by step Solutions of OP Malhotra S.Chand ISC Class-11 Mathematics with Exe-26 (a), 26 (b), With Chapter Test. Visit official Website CISCE for detail information about ISC Board Class-12 Mathematics.

## OP Malhotra Class-11 **Coordinates in 3-Dimensions **S.Chand ISC Maths Solution

Class: | 11th |

Subject: | Mathematics |

Chapter : | Ch-26 Point and their Coordinates in 3-Dimensions of Section -A |

Board | ISC |

Writer | OP Malhotra |

Publications | S.Chand Publications 2020-21 |

–: Select Topics :-

### OP Malhotra Class-11 **Coordinates in 3-Dimensions **S.Chand ISC Maths Solution

**Coordinate Axes**

In three dimensions, the coordinate axes of a rectangular cartesian coordinate system are three mutually perpendicular lines. These axes are called the X, Y and Z axes.

**Coordinate Planes**

The three planes determined by the pair of axes are the coordinate planes. These planes are called XY, YZ and ZX plane and they divide the space into eight regions known as octants.

**Coordinates of a Point in Space**

The coordinates of a point in the space are the perpendicular distances from P on three mutually perpendicular coordinate planes YZ, ZX, and XY respectively. The coordinates of a point P are written in the form of triplet like (x, y, z).

The coordinates of any point on

- X-axis is of the form (x, 0,0)
- Y-axis is of the form (0, y, 0)
- Z-axis is of the form (0, 0, z)
- XY-plane are of the form (x, y, 0)
- YZ-plane is of the form (0, y, z)
- ZX-plane are of the form (x, 0, z)

**How to Plot the Points in Three-dimensional Plane ?**

**The following points illustrate how to plot the points in the three-dimensional coordinate system:**

- Locate the point “x” on the X-axis
- From the point x, moving parallel to the Y-axis, locate the point “y”.
- Similarly, from the determined point, moving parallel to the Z-axis, locate the point “z”.
- This is the final coordinate point in the three-dimensional plane, which we are looking for.

**Important Terms in Three-Dimensional Geometry**

- Three mutually perpendicular lines in space define three mutually perpendicular planes, called Coordinate Planes, which in turn divide the space into eight parts known as Octants and the lines are known as Coordinate Axes;
- Coordinates of a point lying on x-axis, y-axis & z-axis are of the form (x,0,0), (0, y,0) and (0,0, z) respectively;
- Coordinates of a point lying on xy – plane, yz – plane and xz – the plane is of the form (x,y,0), (0,y,z) and (x,0,z) respectively;
- Coordinates of a point P are the perpendicular distances of P from the three coordinate planes YZ, ZX and XY respectively;
- The reflection of the point (x, y, z) in xy – plane, yz – plane and xz plane is (x, y, -z), (-x, y, z) and (x, -y, z) respectively.

Exe-26 (a)

### OP Malhotra Class-11 **Coordinates in 3-Dimensions **S.Chand ISC Maths Solution

Page 26-5

Question 1:

Find the distance from the origin to each of the point

(i)…………

(ii)……….

(iii)……….

(iv)………

Question 2:

…………………

…………………..

…………………

Question 12:

Find the equation of the focus of a point whose distance from the z-axis is equal to its distance from the x-y plane

### Exe-26 (b)

OP Malhotra Class-11 **Coordinates in 3-Dimensions **S.Chand ISC Maths Solution

Page 26-10

Question 1:

Find the coordinates of point which divide the ………………. in the ratio 3 : 4 internally.

Question 2:

…………………..

…………………..

……………………

Question 14:

What is the focus of a point for which

(i)………..

(ii)……….

(iii)……….

(iv)…………

(v)…………

(vi)……….

### Chapter Test

OP Malhotra Class-11 **Coordinates in 3-Dimensions **S.Chand ISC Maths Solution

Page 26-12

-: End of **Coordinates in 3-Dimensions **Solution :-

Return to :- OP Malhotra S. Chand ISC Class-11 Maths Solutions

Thanks

Please share with your friends