class 11 physics vector Laws NEET/JEE

Polygon Law of Vector Addition

If a number of vectors are represented both in magnitude and direction by the sides of a polygon taken in the same order, then the resultant vector is represented both in magnitude and direction by the closing side of the polygon taken in the opposite order.

Properties of Vector Addition

According to the triangle law of vector addition, we have from triangle OPR.

Illustration on subtraction of vectors

(i) A particle is moving at a constant speed in a circular orbit. Find the change in its velocity when it completes half the revolution.

When a particle moves along a circular path with a constant speed than its velocity changes due to a change in direction.

(ii) A car moving towards the south changes its direction towards the west direction with the same speed; Find the change in the velocity of the car.

The magnitude of the change in velocity

The direction of change in velocity,

the change in velocity of the car is along a north-west direction.

Resolution of Vectors

  A.  In two perpendicular components

When a vector is resolved into its components and the components are at right angles to each other then such components are called rectangular components.


Two vectors can be multiplied in the following two ways.

Scalar Product or Dot Product

Dot product or scalar product of two vectors gives the scalar quantity.


Properties of Scalar Product of Dot Product

Vector Product or cross Product

The vector product of two vectors is a vector quantity. The cross product of two vectors is a single vector whose magnitude is equal to the product of the magnitudes of two given vectors multiplied by the sine of the smaller angle between two given vectors.

The direction of the vector given by the cross product of the two vectors is perpendicular to the plane containing the two vectors.

Right-Hand Rule

. Examples: