Question

state and prove the parallelogram law of vector addition. Show how the law enables us to determine analytically the magnitude and direction of resultant of two vectors​

Answer 1

Parallelogram law of vector addition states that

if two vectors are considered to be the adjacent sides of a parallelogram, then the resultant of the two vectors is given by the vector that is diagonal passing through the point of contact of two vectors.

Proof:

Let

A

and

B

are the two vectors be represented by two lines

OP

and

OQ

drawn from the same point. Let us complete the parallelogram and name it as OPTQ. Let the diagonal be

OT

.

Since

PT

is equal and parallel to

OQ

, therefore, vector

B

can also be represented by

PT

.

Applying the triangle's law of vector to triangle OPT.

OT

=

OP

+

PT

⇒

R

=

A

+

B

.

(proved).