Question

Define triangle law of vector addition and
show that vector addition is commutative​

Answer 1

Vector :

A quantity which has both magnitude and direction is said to be an vector quantity

Vector law of addition :

The vector law of addition also known as Triangle law of vector addition and Parallelogram law of Vector addition, states that : When 2 vectors of different directions (which does not include horizontal or vertical directions) are applied on a body, the resultant vector will be the third side of the two vector's triangle formed.

Formula :

$\sf \sqrt{ {a}^{2} + {b}^{2} + 2ab \cos \theta }$

• In parallelograms, the diagonal is the resultant vector.

Since the resultant vector is the diagonal, the following Formula can also be used to find the vector value : $\sf \sqrt{a^{2} + b^{2}}$

Aim :

• To prove that vector law of addition is commutative.

Commutative property :

According to this property,

Any 2 real numbers a and b, are commutative under addition and multiplication.

$\boxed{ \implies \sf a + b = b + a }$

$\boxed{\implies \sf ab = ba}$

Vector law of addition is commutative :-

In the Triangle law of Vector addition, the two vectors are taken as 2 of the triangle's sides and the third side as the resultant vector.

Since for addition, the commutative property is applicable,

The resultant vector = $\sf \sqrt{a^{2} + b^{2}} \:\: (or)\:\: \sqrt{b^{2} + a^{2}}$ The vice versa applies for the second formula too.