1. April 11, 2012 Intro to Vectors Warm-up: Use a math interpretation to describe your spring break or life in general. You could use numbers, symbols, math operations, expressions, equations, equations of graphs, etc. Then write your interpretation underneath. For example, mine would be: y = |x |“My life is V- shaped, sometimes live events bring me down, but family and friends usually help bring me up.”

2. Boat Activity http://illuminations.nctm.org/ActivityDetail.aspx?ID=42

3. April 12, 2012 Magnitude and Operations of Vectors Given x = 1 and y = 1, we have x = y Multiplying each side by,x x 2 = xy Subtracting y 2 from each side x 2 - y 2 = xy - y 2 Factoring each side (x + y)(x - y) = y (x - y) Dividing out the common term (x - y) we have x + y = y Substituting the given values 1 + 1 = 1 Or 2 = 1 What is wrong with this proof?

4. Solution There was nothing wrong up through line (x + y)(x - y) = y (x - y) If we substitute the values of x and y we have (2)(0) = (1)(0) or 0 = 0 However, when we divide both sides by (x - y), we break a fundamental rule of mathematics that we cannot divide out by a fraction which is equal to zero.

5. 6.3a Vectors Vocabulary Initial point – the start of the vector Terminal point – the end of the vector The magnitude is calculated by finding the distance between the initial and terminal point. The direction can be found by finding the slope.

6. Finding the component form and magnitude of a vector The component form of a vector is when the initial point is at the origin (0, 0), written as v = Example 1: Find the component form and magnitude of the vector v that has initial point (4, -7) and terminal point (-1, 5). To find the component form: Subtract the initial point from the terminal point.

7. To find the magnitude ||v||, use the distance formula. The component form of the vector v = So, the magnitude =

8. Example 1: Find the component form and the magnitude of the vector v… a)with an initial point b) Find the component form of (-1, 5) and terminal of the vector A and C. point (15, 12).

9. Unit Vector and Zero Vector A unit vector is when the magnitude/length is equal to 1. A zero vector is when the magnitude/length is equal to 0.

10. How do we get a zero vector? When did the boat stay still?

11. Example 2: Vector Operations adding, subtracting, multiplying Let and Scalar multiple: kv = Find 2v Difference: u – v = u + (-v) = Find: w – v Addition: u + v = Find: v + 2w