Unit 1 Lesson 2 Adding and Subtracting Vectors.notebook...Unit 1 Lesson 2 Adding and Subtracting...
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Unit 1 Lesson 2 Adding and Subtracting Vectors.notebook 1 January 16, 2018 Do NOW! Find the component form and the magnitude of the vector 4EF . E(4, 9) F(1, 1) yes no yes no yes no TI Recall HW Answers
Transcript of Unit 1 Lesson 2 Adding and Subtracting Vectors.notebook...Unit 1 Lesson 2 Adding and Subtracting...
Unit 1 Lesson 2 Adding and Subtracting Vectors.notebook
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January 16, 2018
Do NOW!
Find the component form and the magnitude of the vector 4EF .
E(4, 9) F(1, 1)
yes
no
yes
no
yes
no
T IRecall
HW Answers
Unit 1 Lesson 2 Adding and Subtracting Vectors.notebook
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<2,9> √85
<8, 1> √65
<8, 1> √65
<1, 7> 5√2
<6, 27> 3√85
<2√5, √5> 5
<10, 16> 2√89
Unit 1 Lesson 2
Adding & Subtracting Vectors
• Parallel Vectors• Adding & Subtracting Vectors
Goals
Unit 1 Lesson 2 Adding and Subtracting Vectors.notebook
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Parallel Vectors
Two located vectors AB and PQ are said to be parallel if there is a number
c ≠ 0 such that B A = c(Q P)
and be in the same direction if c > 0, and have opposite directions if c < 0.figure 1 figure 2
P=(3,7) and Q=(4, 2). Let A = (5,1) and B=(16, 14)
Is PQ parallel to AB ?
QP = c(BA) ? IsQP =
BA =
1st find component form:
If C= (5,11) and D=(3, 5) and E=(3, 4) and R = (9, 4)
is CD parallel to EF?
1)
2)
Unit 1 Lesson 2 Adding and Subtracting Vectors.notebook
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Adding Vectors GeometricallyWhen adding vectors geometrically, always link them ...terminal points (head) to initial point (tail).
The resultant vector will start at the original location and end at the terminal point (head) of the final vector.
Unit 1 Lesson 2 Adding and Subtracting Vectors.notebook
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Adding Vectors
The sum of 2 vectors is the resultant.
If they share the same initial point, use equivalent vectors to form a parallelogram. The diagonal is the sum, or resultant.
If they don't share the same initial point, then draw 2 vectors such that the tail of one coincides with the head of the other. Make a triangle by connecting the initial point of 1st to the tail of the 2nd, called the resultant triangle.
To subtract add the opposite.
u
v
)
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The two vectors (the velocity caused by the propeller, and the velocity of the wind) result in a slightly slower ground speed heading a little East of North.If you watched the plane from the ground it would seem to be slipping sideways a little.
Given the following vectors:
u =<2, 4> v=<3, 5> w=<3, 7>
Find
a) u + v b) v + w c) u + w
Unit 1 Lesson 2 Adding and Subtracting Vectors.notebook
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Subtracting Vectors
A = (9, 1) and B = (2, 4). Find C such that C = A B. Then graph A, B, C.
Unit 1 Lesson 2 Adding and Subtracting Vectors.notebook
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Draw the vector A B.
Solution
Solution
w
v
uUse the vectors to geometrically represent 2v + 3u. Pull the tab to check your solution.
Extension
Remember to connect initial points to terminal points!!
Unit 1 Lesson 2 Adding and Subtracting Vectors.notebook
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January 16, 2018
Solution
Solution
w
v
uUse the vectors to geometrically represent -4u + w. Use the line tool to draw the resultant vector. Pull the tab to check your solution.
Extension
w
v
uWrite the vector equation for the following diagram.
w
uu
uvv
r = 2v+3u+werase to reveal answer!
Unit 1 Lesson 2 Adding and Subtracting Vectors.notebook
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HW
Unit 1 Lesson 2
Online
HW
Unit 1 Lesson 2 Adding and Subtracting Vectors.notebook
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January 16, 2018
Start here on Thursday 12/21 after quiz
Quiz on concepts we learned to date on 12/21.
Unit 1 Lesson 2 Adding and Subtracting Vectors.notebook
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January 16, 2018
A = (9, 1) and B = (2, 4). Find C such that C = A B. Then graph A, B, C.
DO NOW!
Draw the vector A B.DO NOW!
Unit 1 Lesson 2 Adding and Subtracting Vectors.notebook
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January 16, 2018
Solution
Solution
w
v
uUse the vectors to geometrically represent 2v + 3u. Pull the tab to check your solution.
Extension
Remember to connect initial points to terminal points!!
Solution
Solution
w
v
uUse the vectors to geometrically represent -4u + w. Use the line tool to draw the resultant vector. Pull the tab to check your solution.
Extension
Unit 1 Lesson 2 Adding and Subtracting Vectors.notebook
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January 16, 2018
w
v
uWrite the vector equation for the following diagram.
w
uu
uvv
r = 2v+3u+werase to reveal answer!
Combining vectors algebraically.
pageNotes
Distribute the scalar quantity.
Combine the xcomponents, then combine the ycomponents.
Unit 1 Lesson 2 Adding and Subtracting Vectors.notebook
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w
v
uUse the vectors to geometrically represent u + 3v + w. Geometrically represent the equation and state the component form of the resultant vector.
**Column form works well for this.
Answer
P = (3, 9) and Q = (4, 2). Let A= (5, 1) and B = (16, 14).
Is PQ parallel to AB ?
Find Q P and B A Is this true? 3(B A) = Q P
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