State and prove parallelogram law of vector addition.

Open in App

Solution

- 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 $\to A$ and $\to B$ are the two vectors be represented by two lines $\to O P$ and $\to O Q$ drawn from the same point. Let us complete the parallelogram and name it as OPTQ. Let the diagonal be $\to O T$ .
Since $\to P T$ is equal and parallel to $\to O Q$ , therefore, vector $\to B$ can also be represented by $\to P T$ .
Applying the triangle's law of vector to triangle OPT.
$\to O T = \to O P + \to P T$
$\Rightarrow \to R = \to A + \to B$ .
(proved).

Suggest Corrections

Similar questions

θ

θ = 0^{0}

θ = 90^{0}

Difference between triangle law and triangle law of vector addition

Join BYJU'S Learning Program