1. A-VM.4. Add and subtract vectors
L6 Magnitude of a vector
A-VM.4. Add and subtract vectors
a. Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.
b. Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.
c. Understand vector subtraction v – w as v + (-w), where -w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.

2. Warm up 1. Write down the following formula: Pythagorean formula
Distance formula
2. How do you find the component of a vector?

3. Magnitude of a vector
Magnitude of a vector from graph:

4. Example Magnitude of a vector from components
eg. Find the magnitude of the vector (5, – 6)

5. Example
Find the Magnitude of a vector from initial and terminal points.
eg. Find the magnitude of the vector AB with initial point A(5, – 6) and terminal point B(– 2, 3).

6. Assignment Find the magnitude of vector = (7, – 3)
Vector has an initial point (4, 1) and a terminal point (– 3, 5).

7. Adding and Subtracting vectors
= (3, – 1)
= (2, 3)

8. Adding and Subtracting vectors
= (3, – 1)
= (2, 3)
By drawing

9. Assignment Find the component of the following vectors:
3. ū = (– 5, 3) ū = (6, 5)
ā = (– 12, –4) ā = (5, 4)
ā – ū = ( , ) ā – ū = ( , )
5. ū = (12, 3)
ā = (– 2, –5)
ā – ū = ( , )

10. Assignment
6. Which vector equation matches the vector operation shown below?

13. 9. Vector u has magnitude 3 and bearing 315o, vector v has magnitude 2 and bearing 180o, vector w has magnitude 3 and bearing 90o.
Use these vectors to sketch the following vectors:
a. u + w
b. u – w
c. u + 2v

14. 10. Make a scale drawing showing the two vectors and their sum.
a. A 9 km trip east followed by a 4 km trip southwest.
b. The heading of a plane is northwest, and its speed is 350km/h. A wind of 50 km/h is blowing from the west.

15. Reflections 1. How do you find the magnitude of a vector?
2. How do you find the sum or difference of 2 vectors?