Vectors Day 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.

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

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

Look!!! u v r u v r

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

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

Scalar Multiplication and Component Form

Examples

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)

Examples

Example

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

Examples