Vectors - Introduction

Description:

Vector quantities

Physical quantities that need both magnitude and direction to completely define them are called Vector quantities.

Scalar quantities

Physical quantities that need only magnitude to completely define them are called Scalar quantities.

Representation of Vectors

• Analytical representation

  a→, A→, b→, B→, etc.. They are the variables with an arrow drawn on top.

Note

1. No matter what the direction of a specific vector is, the arrow is always drawn from left to right on the top of variable name as shown above.

2. In some books, vectors are also represented simply by a bold alphabet (without any arrow on top). E.g. a, A, b, B, etc. They have the same meaning as a→, A→, b→, B→, etc. respectively.

• Pictorial/Diagrammatic representation

  Vectors are shown pictorially by an arrow. Length of the arrow indicates the “magnitude” and direction in which the arrow head is pointing indicates the “direction”.

Magnitude of a vector X→ is indicated by |X|→ or simply X.

Negative of a Vector

Negative of a vector simply reverses the direction of the vector. Magnitude stays unaffected.

Multiplication of a vector by scalar

The magnitude of the vector is multiplied by the scalar. Direction remains unaffected.