Vector Basics
Unit Vectors
Vector Operations
Vector Application
Parametric Equations
100
What qualitites define a vector?
Magnitude and Direction
100
What is the magnitude of every unit vector?
1
100
Find v + u:
v = <3, -3>
u = <4, 9>
<7, 6>
100
Geometrically, how do you add two vectors?
Give both method names:
- Triangle Method (or "Tail-To-Tip")
- Parallelogram Method
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
How do you find magnitude of a vector?
sqrt(a^2+b^2
200
Name two ways to represent a vector algebraically.
1. Component Form -> <a,b>
2. Linear Combination Form -> ai+bj
200
Find v - u:
v = <8, -7>
u = <4, 7>
<4,-14>
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
200
Write in cartesian form:
x = -t^2/3, y = t
x = -y^2/3
300
What is a vector represented on the coordinate plane called?
A directed line segment
300
Find the unit vector in direction v if
v = <-3,2>
<-3sqrt13/13, 2sqrt13/13>
300
Find 3v + 2u:
v = <-2, -2>
u = <5, 4>
<4,2>
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
300
Write in cartesian form:
x = t, y = t^2/6+2t/3-1/3
y = x^2/6+(2x)/3-1/3
400
What is the sum of two vectors called?
A resultant
400
Find the unit vector in direction v if
v = <3,-4>
Must be in linear combination form
3/5i-4/5j
400
Find vector RS if
Point R -> (6,9)
Point S -> (12, 13)
<6, 4>
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
400
Write in cartesian form:
x = 2cos(t), y = 4sin(t)
x^2/4+y^2/16=1
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|>
500
Find the unit vector in direction v if
v = -3i - 5j
<-3sqrt34/34, 5sqrt34/34>
500
Find Magnitude of v + u:
v = <-8, -2>
u = <3, 10>
13
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
500
FINAL JEOPARDY
FINAL JEOPARDY