**Table Of Contents**

AKTU Btech Unit 01 COORDINATE SYSTEMS covers numerous coordinate systems, transformations, vector operations, and their applications in geometry, physics, and engineering. Improve spatial representation and problem-solving abilities.

Dudes 🤔.. You want more useful details regarding this subject. Please keep in mind this as well.Important Questions For Electromagnetic Field Theory:*Unit-01 *Unit-02 *Unit-03 *Unit-04 *Unit-05 *Short-Q/Ans *Question-Paper with solution 21-22

**Q1. What is a dot product ?.Also mention its properties and applications. **

**Ans. A. Scalar (or Dot) product:**

1. The scalar or dot product of the two vectors **A and B _{(you can take reference from image how to write vector A and B)} **is defined as the product of the magnitude of

**, the magnitude of**

_{vector}A**and the cosine of the smaller angle between them.**

_{vector}B**B. Properties of dot product: **

1. If the two vectors are parallel to each other, i.e. 𝝷 = 0° then cos 𝝷_{AB} =1

**C. Applications of dot product: **

1. To find the angle between the two vectors.

3. Physically, work done by a constant force **Vector F** over a straight displacement **Vector d** can be expressed as a dot product of two vectors.

**Q2. What is a cross product ? Also mention its properties. **

**Ans. A. Cross (or vector) product: **

1. The cross or vector product is defined as the product of the magnitudes of ** **vectors **A and B _{(you can take reference from image how to write vector A and B)}** and the sine of the smaller angle between

**vectors**

**A and B**But this product is a vector quantity and has a direction perpendicular to the plane containing the two vector

**vectors**

**A and B .**

**B. Properties of cross product: **

1. Two vectors are considered parallel if their cross product is zero.

**3. Cross product in determinant form: **Consider the two vector in the cartesian system as,

**Q3. Write a short note on cartesian coordinate system. **

**Ans. **1. It is also known as rectangular coordinate system.

2. In rectangular coordinate system, three coordinate axis, i.e., x, y and z are set up mutually at right angles to each other.

3. A point Pin cartesian coordinate system is represented by P(x,y,z).

4 The ranges of the coordinate variables x, y and z are

**Q4. Give a brief description on cylindrical coordinate system ?**

**Ans. A. Cylindrical coordinate system: **

1. A point P (ρ, ф, z) in cylindrical coordinate system represents p the radius of the cylinder, ф the azimuthal angle and z is same as in cartesian system.

2. The ranges of variables ρ, ф and z are

**B. Relation between cartesian and cylindrical ocoordinate system: **

**Q5. Convert a point P(4, -3, 6) and a vector R = z a**_{x}** + y a**_{z}** into cylindrical coordinate systems.**

_{x}

_{z}

**Ans. **1. At point P, x = 4, y =-3, 2 = 6

**Q6. Describe the gradient of a scalar field. **

**Ans. A. Gradient of scalar field: **

1. The gradient of a scalar field M is a vector that depicts the maximum rate of increase of M in space in terms of both magnitude and direction.

2. The operation of the ▽(del) operator on a scalar function is called gradient of a scalar

**B. Properties of gradient of scalar:**

- 1. The gradient ▽M gives the maximum rate of change of M per unit distance.
- 2. The gradient ▽M always indicates the direction of the maximum rate of change of M.
- 3.The gradient ▽M at any point is perpendicular to the constant M surface, which passes through the point.
- 4. The directional derivative of M along the unit vector a is ▽M. a , which is projection of ▽M in the direction of unit vector a.

**Important Question with solutions | AKTU Quantums | Syllabus | Short Questions**

**Electromagnetic Field Theory** Btech Quantum PDF, Syllabus, Important Questions

**Electromagnetic Field Theory**Btech

Label | Link |
---|---|

Subject Syllabus | Syllabus |

Short Questions | Short-question |

Important Unit-1 | Unit-1 |

Important Unit-2 | Unit-2 |

Important Unit-3 | Unit-3 |

Important Unit-4 | Unit-4 |

Important Unit-5 | Unit-5 |

Question paper – 2021-22 | 2021-22 |

**Electromagnetic Field Theory** Quantum PDF | AKTU Quantum PDF:

Quantum Series | Links |

Quantum -2022-23 | 2022-23 |

## AKTU Important Links | Btech Syllabus

Link Name | Links |
---|---|

Btech AKTU Circulars | Links |

Btech AKTU Syllabus | Links |

Btech AKTU Student Dashboard | Student Dashboard |

AKTU RESULT (One VIew) | Student Result |

## Important Links-Btech (AKTU)

** **

## 5 thoughts on “Unit 01 COORDINATE SYSTEMS Important Question Answer AKTU Btech”