Properties of Vector Addition

. Also, the length or the magnitude of a vector cannot be negative. In this article, we are going to learn the two important properties of vector addition in detail.

Two Properties of Vector Addition

We know that the vector addition is the sum of two or more vectors. Two important laws associated with vector addition are triangle law and parallelogram law. Similarly, the properties associated with vector addition are:

• Commutative Property
• Associative Property

Now, let us discuss the two properties of vector addition in detail.

Commutative Property of Vector Addition

The commutative property of vector addition states that “For any two vectors,

\vec\end \) \(\begin\vec\end \) \(\begin\vec\end \)

Proof:

Consider a parallelogram ABCD as shown in the figure.

\(\begin|\overline|\end \) \(\begin|\overline|\end \) \(\begin\vec\end \)

Now, by using the triangle law of vector addition from the triangle ABC, we can write:

\(\begin\overline=\vec+\vec\end \)

Since, the opposite sides of a parallelogram are parallel and equal, we have

\(\begin|\overline|\end \) \(\begin|\overline|\end \) \(\begin\vec\end \)

Now, again use the triangle law from the triangle ADC, we get