Vectors Day 2 Scalar Multiplication A vector can

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 r v u

Look!!! u v r r u v

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