Slide 1 / 159 Slide 2 / 159 Pre-Calculus Vectors 2015-03-24 - PowerPoint PPT Presentation

Slide 62 / 159 Scalar Multiples 37 Given vector =(4, 5) what is Teacher Teacher (8/3 , 10/3) A (2 , 7/3) B (16/3 , 25/3) C (8/3, 7/3) D

Slide 63 / 159 Scalar Multiples 38 Given vector =(4, 5) what is Teacher Teacher (1 , 2) A (12 , 15) B (-12 , 15) C (-12, -15) D

Slide 64 / 159 Scalar Multiples Teacher Teacher 39 Given find

Slide 65 / 159 Addition Return to Table of Contents

Slide 66 / 159 Addition Vector Addition

Slide 67 / 159 Addition Vector Addition Methods Tail to Tip Method

Slide 68 / 159 Addition Vector Addition Methods Teacher Teacher Move the vectors to represent the following operation. Draw the resultant vector.

Slide 69 / 159 Addition Vector Addition Methods Parallelogram Method Place the tails of each vector against one another. If you finish drawing the parallelogram with dashed lines and draw a diagonal line from the tails to the other end of the parallelogram to find the vector sum.

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Slide 71 / 159 Addition Teacher Teacher Given Find the resultant vector:

Slide 72 / 159 Addition Teacher Teacher 40 What is the resultant vector for if (5 , 5) A (4 , 6) B (5 , 6) C (4 , 5) D

Slide 73 / 159 Addition Teacher Teacher 41 What is if

Slide 74 / 159 Addition Teacher Teacher 42 The components of vectors are given as follows: and Solve for the magnitude of A 5 B #17 C 17 D 10 E 8

Slide 75 / 159 Subtraction Return to Table of Contents

Slide 76 / 159 Subtraction Anti- Parallel Vectors

Slide 77 / 159 Subtraction Teacher Teacher

Slide 78 / 159 Subtraction Vector Addition Method for Subtraction Teacher Teacher Draw the vectors to represent the following operation. Draw the resultant vector.

Slide 79 / 159 Subtraction Vector Addition Method for Subtraction Teacher Teacher Draw the vectors to represent the following operation. Draw the resultant vector.

Slide 80 / 159 Subtraction Vector Addition Method for Subtraction Teacher Teacher Draw the vectors to represent the following operation. Draw the resultant vector.

Slide 81 / 159 Subtraction Vector Addition Method for Subtraction Teacher Teacher Draw the vectors to represent the following operation. Draw the resultant vector.

Slide 82 / 159 Subtraction Teacher Teacher 43 D A C B

Slide 83 / 159 Subtraction 44 Teacher Teacher D A C B

Slide 84 / 159 Subtraction 45 Teacher Teacher C D A B

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Slide 86 / 159 Subtraction Given Teacher Teacher Find the resultant vector:

Slide 87 / 159 Subtraction 46 What is the resultant vector for if Teacher Teacher (3 , 1) A (-3 , -1) B (5 , 5) C (3 , -1) D

Slide 88 / 159 Subtraction Teacher Teacher 47 What is if

Slide 89 / 159 Subtraction 48 The components of vector A and B are given as follows: Teacher Teacher The magnitude of B-A, is closest to: A 10.17 B 4.92 C 2.8 D 9.7 E 25

Slide 90 / 159 Vector Equations of Lines Return to Table of Contents

Slide 91 / 159 Vector Equations of Lines Vector Equation for a Line Consider the line R through R and S. There is a unique congruent vector, in standard S position. The difference between any two points on the line is where t is a real number.

Slide 92 / 159 Vector Equations of Lines Teacher Teacher Vector Equation for a Line Example: Find the equation of the line through R(2,6) and is parallel to v. R S

Slide 93 / 159 Vector Equations of Lines Draw a graph of the line through (2, 7) and parallel to v=(1,4) Teacher Teacher Write the equation of the line. Write the equation of the line in parametric form.

Slide 94 / 159 Vector Equations of Lines Teacher Teacher Draw a graph of the line through (3, -7) and parallel to v=(-2,6) Write the equation of the line. Write the equation of the line in parametric form.

Slide 95 / 159 Vector Equations of Lines 49 Which of the following is the vector equation of the line Teacher Teacher through (-3, -4) and parallel to u=(6, 1)? (x+4, y+3) = t(6,1) A (x-4, y-3) = t(6,1) B (x+3, y+4) = t(6,1) C (x-3, y-4) = t(6,1) D

Slide 96 / 159 Vector Equations of Lines 50 Which of the following is parametric form of the equation of the line through (-3, -4) and parallel to u=(6, 1)? Teacher Teacher A C B D

Slide 97 / 159 Vector Equations of Lines 51 Which of the following is the vector equation of the line through (5, 2) and parallel to u=( -7, 1)? Teacher Teacher (x -1, y+7) = t(5,2) A (x+7, y-1) = t(5,2) B (x+5, y+2) = t(-7,1) C (x-5, y-2) = t(-7,1) D

Slide 98 / 159 Vector Equations of Lines 52 Which of the following is parametric form of the equation of the line through (5, 2) and parallel to u=( -7, 1)? Teacher Teacher A C D B

Slide 99 / 159 Vector Equations of Lines Given two points (x 1 ,y 1 ) and (x 2 ,y 2 ), the parametric equations of Teacher Teacher the line are: x = x 1 + t*(x 2 - x 1 ) y = y 1 + t*(y 2 - y 1 ) Find the parametric equation of the line through (4, 7) and (2, 8)

Slide 100 / 159 Vector Equations of Lines Find the parametric equation of the line through (3, -5) and (8, 9) Teacher Teacher