Vectors

A study of motion will involve the introduction of a variety of quantities, which are used to describe the physical world. Examples of such quantities are distance, displacement, speed, velocity, acceleration, mass, momentum, energy, work, power etc. All these quantities can be divided into two categories – scalars and vectors. The scalar quantities have magnitude only. It is denoted by a number and unit. Examples: length, mass, time, speed, work, energy, temperature etc. Scalars of the same kind can be added, subtracted, multiplied or divided by ordinary laws. The vector quantities have both magnitude and direction. Examples: displacement, velocity, acceleration, force, weight, momentum, etc.

Types of Vectors
i. Unit Vector

ii. Null vector or zero Vector
iii. Equal Vector
iv. Negative Vector
v. Parallel Vector
vi. Collinear Vector
vii. Coplanar Vector

Triangle Law of vector addition

If two vectors are represented in magnitude and direction by the two adjacent sides of a triangle taken in order, then their resultant is the closing side of the triangle taken in the reverse order.

 Parallelogram law of vector addition

If two vectors acting at a point are represented in magnitude and direction by the two adjacent sides of a parallelogram, then their resultant is represented in magnitude and direction by the diagonal passing through the common tail of the two vectors.

Scalar Product and Vector Product

Example1

Example2

Example 1

Geometrical Meaning

Applications of Dot product and Cross product of vectors