Adding Vectors Along a Straight Line

Position-Displacement :: | :: Adding on an Angle

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Scale Diagram Method

When adding vector quantities like displacement, you have to be aware of the magnitude and the direction of the vectors you are adding. You can show this by using the "head to tail" method.

You must join the "head" end of one vector to the "tail" end of the next vector.

Scale Diagram Method
1. State the direction (e.g., with a compass rose)
2. List the givens and indicate what variable is being solved
3. State the scale to be used (e.g., 1 cm = 5 km)
4. Draw one of the initial vectors to scale
5. Draw the second vector to scale using the head of the first vector as a starting point.
6. Repeat step 5 for each additional vector but use the head of the previous vector as a starting point
6. Draw and label the resultant vector
7. Measure the resultant vector and find the length using your scale
8. Write a statement including both the magnitude and the direction of the resultant vector



Steps 7 & 8 can be done after you finish measuring the resultant vector using the scale.

Adding Vectors Algebraically

When adding vectors algebraically, we must assign positive or negative numbers according to the direction (the most common convention is making north and east positive while making south and west negative). For example, say you are given two vector quantities, 250 m north and 150 m south, you could make north a positive number while south would be assigned as negative (making the vectors 250 m and -150 m, respectively).

Summary of Algebraic Method
1. Indicate which direction is positive and which is negative
2. List the given information and indicate what variable is being solved

3. Write the equation for adding the vectors

4. Substitute numbers (with correct signs) into the equation, and solve
5. Write a statement with your answer (including magnitude and direction)

Algebraic Method for Adding Vectors - Sample #1

1. Let north be postive and south be negative

2.
1 = 250 m [N] = +250 m
2 = 150 m [S] = -150 m

3. r = 1 + 2

4. r = (+250 m) + (-150 m) = +100 m

5. The total resultant displacement is 100 m [N]

Continue to the next lesson: Vectors at an Angle