2.11 Resultant Vector

Definition

A resultant vector is a single vector that has the same effect as two or more vectors acting together.

Instead of representing each vector separately, they can be replaced by one equivalent vector called the resultant vector.

The resultant vector is commonly represented by $\vec{R}$.

Obtaining the Resultant Vector

The resultant vector is obtained by combining vectors.

Depending on the situation, it can be found by:

• vector addition,
• vector subtraction, or
• adding vector components.

The resultant vector can be obtained using any of these methods.

Example

A student walks 3 m east and then 4 m north.

The two displacements can be replaced by a single vector drawn from the starting point to the final position.

This vector is called the resultant displacement because it represents the overall effect of both displacements.

The resultant displacement has a magnitude of 5 m and points from the starting position to the final position.

Key Points

• A resultant vector is a single vector that represents the combined effect of two or more vectors.
• A resultant vector has both magnitude and direction.
• A resultant vector can be found using vector addition, vector subtraction, or vector components.
• The resultant vector represents the overall effect of all the vectors acting together.