Take an online course in Precalculus. All Rights Reserved.

Click to view content. Forces are vectors and add like vectors, so the total force on the third skater is in the direction shown. Vectors--unlike simple numbers scalars that have only a magnitude--have both a magnitude length and direction.

## 5.1 Vector Addition and Subtraction: Graphical Methods

Use a protractor to measure the direction of R. We start by choosing a coordinate system with its x-axis parallel to the velocity of the river.

In the next section, we cover how to solve this type of problem analytically. The vector or Cross Product the result is a vector.

A boat attempts to travel straight across a river at a speed of 3. Draw the vectors one after another, placing the initial point of each successive vector at the terminal point of the previous vector. We will explore how to represent vector quantities, as well as how to add and subtract them. Strategy We can represent the first leg of the trip with a vector A , and the second leg of the trip that she was supposed to take with a vector B.

## Adding and Subtracting Vectors

Rearrange the vectors in any order head-to-tail and compare. Texas Gateway: This video shows four graphical representations of vector addition and matches them to the correct vector addition formula.

Changing the order does not change the resultant. Note that the "head" and "tail" of a vector are defined as shown below.

The diagonal from the initial point to the opposite vertex of the parallelogram is the resultant. Using its magnitude and direction, this vector can be expressed as.

Strategy We start by choosing a coordinate system with its x-axis parallel to the velocity of the river.

And now you know why numbers are called "scalars", because they "scale" the vector up or down. True or FalseāThe more long, red vectors you put on the graph, rotated in any direction, the greater the magnitude of the resultant green vector.