Question

Below is a graph with two vectors shown on it.
Add them, and then draw the resultant vector on the graph in standard position.

Now, find the magnitude of the resultant vector.

Answer and Detailed Explanation

Step 1: Understand the Concept

We will use the Parallelogram Law of Vector Addition:
If two vectors are represented by two adjacent sides of a parallelogram, then the diagonal from their common point represents the resultant vector.

Step 2: Visualize and Construct the Parallelogram

The vectors OA and OB are shown as adjacent sides.
To complete the parallelogram:

• From point A, draw a line parallel and equal in length to vector OB.
• From point B, draw a line parallel and equal to vector OA.
• Connect the endpoints to form a complete parallelogram OACB.

Step 3: Measure the Resultant Vector

The length of vector OC (measured using the scale of the graph) is found to be:
|R| = 6.7 units

Therefore, the magnitude of the resultant vector is 6.7 units.