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Vector Algebra & Cartesian Coordinate System- 1 Video Lecture | Crash Course for IIT JAM Physics

FAQs on Vector Algebra & Cartesian Coordinate System- 1 Video Lecture - Crash Course for IIT JAM Physics

1. What is the difference between a vector and a scalar?

Ans. A vector is a quantity that has both magnitude and direction, such as displacement or velocity. On the other hand, a scalar is a quantity that has only magnitude, such as distance or speed.

2. How do you represent a vector in Cartesian coordinate system?

Ans. In a Cartesian coordinate system, a vector is represented by its components along the x, y, and z axes. These components can be represented as a triplet (x, y, z) or as a column matrix [x, y, z].

3. What are the basic operations in vector algebra?

Ans. The basic operations in vector algebra include addition, subtraction, scalar multiplication, dot product, and cross product. Addition and subtraction are performed component-wise, scalar multiplication scales the magnitude of the vector, dot product gives a scalar quantity, and cross product gives a vector perpendicular to the two input vectors.

4. How can vectors be combined using vector algebra?

Ans. Vectors can be combined using vector algebra through various operations. Addition of vectors results in the formation of a new vector with the sum of their components. Subtraction of vectors results in the formation of a new vector with the difference of their components. Scalar multiplication scales the magnitude of the vector. Dot product and cross product combine vectors to give scalar and vector quantities, respectively.

5. What is the significance of the magnitude and direction of a vector?

Ans. The magnitude of a vector represents its size or length, providing information about the quantity or value it represents. The direction of a vector indicates the orientation or angle at which it is pointing. Both magnitude and direction are crucial in fully describing a vector and understanding its physical meaning or application.

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Sep 21, 2025 Last updated

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