Question

Prove that the parallelogram law of vector addition??

Answer 1

Parallelogram Law of Vector Addition states that when two vectors are represented by two adjacent sides of a parallelogram by direction and magnitude then the resultant of these vectors is represented in magnitude and direction by the diagonal of the parallelogram starting from the same point

Answer 2

$\large \bf{\green{Parallelogram\: Law\: Of\: Vector\: Addition}}$

$\LARGE \text{STATEMENT :-}$

☛ If Two vectors acting at a point are represented both in magnitude and direction by the two adjacent sides of the parallelogram ,then their resultant can be completely represented by the diagonal drawn from the same point .

$\LARGE \text{EXPLAINATION :-}$

☛ Consider two vectors $\vec{A} + \vec{B}$ are represented by the two adjacent sides of the parallelogram as shown in the figure (1 ).

☛ Then their resultant can be represented by the diagonals drawn from the same point as shown in the figure (2).

☛ Hence , Graphically, the resultant

☛ $\vec{R} = \vec{a} + \vec{b}$