Precalculus - Unit 5 Review

Vector Basics

100

What qualitites define a vector?

Magnitude and Direction

200

How do you find magnitude of a vector?

sqrt(a^2+b^2

300

What is a vector represented on the coordinate plane called?

A directed line segment

400

What is the sum of two vectors called?

A resultant

500

What is and how do you find a unit vector in the direction of the original vector?

The vector of magnitude 1 in the same direction.

Divide each component by the vector's magnitude.

V =

<a/|v|, b/|v|>

Unit Vectors

100

What is the magnitude of every unit vector?

1

200

Name two ways to represent a vector algebraically.

1. Component Form -> <a,b>

2. Linear Combination Form -> ai+bj

300

Find the unit vector in direction v if 

v = <-3,2>

<-3sqrt13/13, 2sqrt13/13>

400

Find the unit vector in direction v if 

v = <3,-4>

Must be in linear combination form

3/5i-4/5j

500

Find the unit vector in direction v if 

v = -3i - 5j

<-3sqrt34/34, 5sqrt34/34>

Vector Operations

100

Find v + u:

v  = <3, -3>

u  = <4, 9>

<7, 6>

200

Find v - u:

v  = <8, -7>

u  = <4, 7>

<4,-14>

300

Find 3v + 2u:

v  = <-2, -2>

u  = <5, 4>

<4,2>

400

Find vector RS if 

Point R -> (6,9)

Point S -> (12, 13)

<6, 4>

500

Find Magnitude of v + u:

v  = <-8, -2>

u  = <3, 10>

13

Vector Application

100

Geometrically, how do you add two vectors?

Give both method names:

- Triangle Method (or "Tail-To-Tip")

- Parallelogram Method

200

A metal ball lies on a flat horizontal surface. It is attracted by two magnets placed around it.

The first magnet's force on the ball is 1N in a direction that is a 60 degree rotation from east.

The second magnet's force on the ball is 2N in a direction that is a 160 degree rotation from east.

What direction is the ball being pulled in by both?

theta = tan^-1(1.55/-1.38) + 180

132  degrees

300

A boat is travelling at a speed of 20 mph in a direction that is a 210 degree rotation from east.

At a certain point it encounters a current at a speed of 12 mph in a direction that is a 40 degree rotation from east.

What is the boat's speed after meeting the current?

8.4 mph

400

A ship is heading due north at 20 km/h but is blown off course by the wind which is blowing from 30° west of south at 5 km/h. 

Find the resultant speed and direction of the ship?

24.45 kmph in a direction 84.13 degrees East of North

500

Sam and Alex are pulling a box. Sam pulls with 120 Newtons of force at 30°
Alex pulls with 100 Newtons of force at 45° as shown. What is the combined force and direction? 

174.95 N, in a direction of -3.5 degrees

Parametric Equations

100

What is the letter we use to represent our third parameter in a parametric equation and what is it typically understood to represent?

t, time

200

Write in cartesian form:

x = -t^2/3, y = t

x = -y^2/3

300

Write in cartesian form:

x = t, y = t^2/6+2t/3-1/3

y = x^2/6+(2x)/3-1/3

400

Write in cartesian form:

x = 2cos(t), y = 4sin(t)

x^2/4+y^2/16=1

500

FINAL JEOPARDY

FINAL JEOPARDY