Today in Precalculus

1. Today in Precalculus • Notes: Vector Operations • Go over homework • Homework

2. Vector Operations • Vector Addition • Vector multiplication (multiplying a vector by a scalar or real number) Let u= u1,u2 and v=v1,v2 and k be a real number (scalar). Then: 1. The sum of vectors u and v is the vector u+v = u1,u2+ v1,v2=u1+v1,u2+v2 2. The product of the scalar k and the vector u =ku = ku1,u2=ku1,ku2

3. Geometric representation of vector addition v u u+v u+v u parallelogram Tail-to-head v

4. Geometric representation of vector multiplication The product ku can be represented by a stretch or shrink of u by a factor of kwhen k>0. If k<0, then u also changes direction. u 2u ½u -u -½u

5. Example Let u= -3,2 and v = 2,5. Find the component form of the following vectors: a) u + v, b) 2u, c) 3u-v a) Using component form definition of sum of vectors: u + v =-3,2 + 2,5 = -3+2,2+5 = -1,7 Geometrically: start with -3,2 and move right 2 and up 5

6. Example • Using component form definition of scalar: 2u = 2-3,2=-6,4

7. Example c) Using the component form definitions: 3u – v = 3-3,2 – 2,5 = -9,6 – 2,5 = -11,1 or 3u + (–v) = 3-3,2 + (–1)2,5 = -9,6 + -2,-5 = -11,1

8. Example u + v u + (-1)v u – w 3v

9. Example 2u + 3w 2u – 4v -2u –3v -u – v

10. Homework Pg 511: 9-20 all