6.3 Vectors in a Plane

Objective: 1) Perform operations with vectors, both graphically and algebraically.2) Apply vectors in real-life situations.

Standard: Linear Algebra 7.0

What's a Vector?

_____________

_____________

It's got _________ and _____________!Terminal – Initial

Ways to represent vectors:Component Form:

Linear Form:

Trigonometric Form:

On the Moodle Discussions:Don't use < and > for vectors. Use LaTeX.

$$\langle{-3,5}\rangle$$

$$\|v\|$$

Finding a vector:Ex. 1) Find the component form and magnitude of the vector v that has an initial point of (–2, 3) and terminal point (–7, 9).

Ex. 2) Let u be the vector with initial point (–2, 6) and terminal point (–8, 3). Write u as a linear combination of the standard unit vectors i and j.

Vector Operations:Ex. 3) Find the following if …a) u–v

b) 3v–2u

Graphing Vectors:Ex. 3b) Graph the following if …a) u+v

b) 3v–2u

Ex. 4) Let u = i + j and v = 5i - 3j. Find 3u - 2v.

Direction AnglesEx. 5) Find the direction angle.a) -6i+6j

b)

Trigonometric FormJust like _____, ______, and ______ can be used to represent a location on a plane, also _____, _____, and _____________ can be used in the same way.

Ex. 6) Write in trig form.

Assignment:

#8 p. 456 #3-13 (odd), 21-33 (odd), 45-66 (mult. of 3)