Addition of vectors

Resultant of vectors 

When two or more vectors are added to produce only one vector, the result of the  vectors is called the Resultant of the vectors.

Example

What is the resultant of vector A and B  ( in fig 1 above) acting :

1. In the same direction
2. Opposite direction
3. Both at an angle N60E to each other

What will be the resultant if A ACTS TOWARD WEST and B at N30E ?

Take A=20N and B = 30N

SOLUTIION

1.

See fig 1& 2 above

      The resultant of two vectors acting in the same direction is the sum of the magnitude of the vectors and the resultant direction is the direction of the two vectors. See fig1

R = A+B   = 20+30 =50N alond same direction with Aand B

ii

The resultant of two vectors acting in the opposite direction is the difference in the magnitude of the vectors and the resultant direction is the direction of the  vector with larger magnitude. See fig 2

R=B-A in the direction of B

R= 30-20 =10N along B

EQUAL VECTORS

Same direction

If A=B  then R=A+B  along A and B

Opposite direction

If A=B then R=0 and the system will be in equilibrium

iii    solution see parallelogram law of vector for solution to question iii