Ask a Teacher

Vectors

Vector Quantities : The physical quantities which have magnitude as well as direction, are called the vector quantities. They are added  and subtracted according to special laws such as parallelogram law of addition, triangle law of addition.

Examples : Displacement, velocity, acceleration, momentum, force, moment of a force (or torque), impulse, weight, temperature gradient, electric field, magnetic field, dipole moment etc.

Types of vectors

(i)Zero vector

Zero vector is that vector which has zero magnitude and an arbitrary direction. A zero vector is represented by . It is also called a null vector.

The main properties of a zero vector

1.Zero or null vectors are taken to be equal and their directions are quite arbitrary and indeed quite immaterial.

2.The result of adding a zero vector to any vector is the vector itself.

3.The result of multiplication of a real number with zero vector is a zero vector itself and the result of multiplication of and a vector gives a zero vector.

4.The result of addition of a vector to its own negative vector is a zero vector.

Examples of zero vector :

(1) The velocity vector of a stationary object is a zero vector.

(2) The acceleration of an object moving with uniform velocity is a zero vector.

(3) The displacement of a stationary object is a zero vector.

8. Explain about any three types of vectors

(ii) Equal Vectors

Two vectors are said to be equal when they are identical both in magnitude and direction.

In the figure given below the vectors have the same magnitude and direction. Therefore are equal vectors.

(iii)Like Vectors

Two vectors are said to be like vectors, if they have same direction but different magnitudes.

(iv) Unit Vector

It is a vector of unit magnitude drawn in the direction of a given vector. A unit vector is the direction of is written as  and is read as 'A cap'. It is used to specify a given direction. Thus we have,

In Cartesian coordinates and are unit vectors along x, y and z axes respectively. They are called orthogonal unit vectors.