1. Vectors Day 2

2. Scalar Multiplication A vector can be multiplied by a real number Multiplying a vector by a positive number changes its size, but not its direction. Multiplying a vector by a negative number changes its direction and its size (unless it is multiplied by -1) The multiplication of a scalar, k, and a vector, v, is denoted as kv A scalar “scales” the size of the vector.

3. Adding vectors – “The Triangle Method” The process of geometrically adding two vectors is as follows: Given vector v and vector u 1)Draw vector v 2)At the terminal point of v, draw vector u 3)Draw the resultant vector (r) from the initial point of v to the terminal point of u

4. Examples 1. v + u 2. u + v u v r u v r

5. Look!!! u v r u v r

6. Example: Subtraction 4. u - v u v r v

7. Adding vectors in component form Find the component form of the resultant vector.

8. Scalar Multiplication and Component Form

9. Examples

10. Unit vectors To find the unit vector of any non- vertical or non-horizontal vector: 1.Find the magnitude of the vector 2.Multiply the vector by the reciprocal of its magnitude (basically divide the vector by its magnitude to give it a length of 1) 3.Perform the scalar multiplication on the appropriate form of the vector (the form the problem was written in)

11. Examples

12. Example

13. Assignment #2 6.3 Exercises #13-22, 25-28,35-40, 45-46

14. Examples