Find the angle $\theta$ between the vectors. $\begin{array} { l } \mathbf { u } = \langle 4,0 \rangle \\ \mathbf { v } = \langle 0 , - 3 \rangle \end{array}$ (Round the answer to 1 decimal place. )

A) $30 ^ { \circ }$ B) $110 ^ { \circ }$ C) $70 ^ { \circ }$ D) $105 ^ { \circ }$ E) $90 ^ { \circ }$ A) $30 ^ { \circ }$ B) $110 ^ { \circ }$ C) $70 ^ { \circ }$ D) $105 ^ { \circ }$ E) $90 ^ { \circ }$

Find the dot product of u and v. \[\begin{array} { l } \mathbf { u } = \langle 5,1 \rangle \\ \mathbf { v } = \langle - 2,4 \rangle \end{array}\]

A) -10 B) -8 C) -4 D) -6 E) -2 A) -10 B) -8 C) -4 D) -6 E) -2

Find the dot product of u and v. \[\begin{array} { l } \mathbf { u } = \langle - 4,9 \rangle \\ \mathbf { v } = \langle - 2 , - 5 \rangle \end{array}\]

A) -41 B) -33 C) -37 D) -35 E) -39 A) -41 B) -33 C) -37 D) -35 E) -39

Find the dot product of u and v. \[\begin{array} { l } \mathbf { u } = \langle 6,14 \rangle \\ \mathbf { v } = \langle - 2,2 \rangle \end{array}\]

A) 18 B) 14 C) 20 D) 12 E) 16 A) 18 B) 14 C) 20 D) 12 E) 16

Find the projection of u onto v. $\begin{array} { l } \mathbf { u } = \langle 3,6 \rangle \\ \mathbf { v } = \langle 4,6 \rangle \end{array}$

A) $13 \langle 72,48 \rangle$ B) $\frac { 1 } { 13 } \langle 3,4 \rangle$ C) $\frac { 13 } { 12 } \langle 48,72 \rangle$ D) $\frac { 1 } { 13 } \langle 48,72 \rangle$ E) $\frac { 12 } { 13 } \langle 48,72 \rangle$ A) $13 \langle 72,48 \rangle$ B) $\frac { 1 } { 13 } \langle 3,4 \rangle$ C) $\frac { 13 } { 12 } \langle 48,72 \rangle$ D) $\frac { 1 } { 13 } \langle 48,72 \rangle$ E) $\frac { 12 } { 13 } \langle 48,72 \rangle$

Find the dot product of u and v. \[\begin{array} { l } \mathbf { u } = 6 \mathbf { i } + 4 \mathbf { j } \\ \mathbf { v } = 8 \mathbf { i } - 2 \mathbf { j } \end{array}\]

A) 36 B) 40 C) 44 D) 42 E) 38 A) 36 B) 40 C) 44 D) 42 E) 38

Exam 39:Vectors and Dot Products

Use the vectors $\mathbf { u } = \langle 3,5 \rangle$ , $\mathbf { v } = \langle - 2,2 \rangle$ ,and $\mathbf { w } = \langle 5 , - 3 \rangle$ to find the indicated quantity.State whether the result is a vector or a scalar. $( 3 \mathbf { w } \cdot \mathbf { v } ) \mathbf { u }$

(Multiple Choice)

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Question 21

Find the angle $\theta$ between the vectors. =\langle4,0\rangle =\langle0,-3\rangle (Round the answer to 1 decimal place. )

(Multiple Choice)

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Question 22

Find the projection of u onto v if $\mathbf { u } = \langle 4 , - 5 \rangle$ , $\mathbf { v } = \langle 3 , - 1 \rangle$

(Multiple Choice)

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Question 23

Use the dot product to find the magnitude of u. $\mathbf { u } = 35 \mathbf { i } + 40 \mathbf { j }$

(Multiple Choice)

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Question 24

Find the dot product of u and v. =\langle5,1\rangle =\langle-2,4\rangle

(Multiple Choice)

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Question 25

Given $\mathbf { u } = - \mathbf { i } + 3 \mathbf { j }$ and $\mathbf { v } = 5 \mathbf { i } + 4 \mathbf { j }$ ,find $u^.v$

(Multiple Choice)

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Question 26

Find the dot product of u and v. =\langle-4,9\rangle =\langle-2,-5\rangle

(Multiple Choice)

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Question 27

Find the dot product of u and v. =\langle6,14\rangle =\langle-2,2\rangle

(Multiple Choice)

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Question 28

Find the angle between the vectors u and v. $\mathbf { u } = \cos \left( \frac { \pi } { 3 } \right) \mathbf { i } + \sin \left( \frac { \pi } { 3 } \right) \mathbf { j }$ , $v = \cos \left( \frac { 3 \pi } { 4 } \right) i + \sin \left( \frac { 3 \pi } { 4 } \right) j$

(Multiple Choice)

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Question 29

Use the vectors $\mathbf { u } = \langle 2,4 \rangle$ , $\mathbf { v } = \langle - 4,5 \rangle$ ,and $\mathbf { w } = \langle 5 , - 4 \rangle$ to find the indicated quantity.State whether the result is a vector or a scalar. $( \mathbf { u } \cdot 2 \mathbf { v } ) \mathbf { w }$

(Multiple Choice)

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Question 30

Use the dot product to find the magnitude of u. $\mathbf { u } = 4 \mathbf { j }$

(Multiple Choice)

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Question 31

Use vectors to find the measure of the angle at vertex B of triangle ABC,when $A = ( 5,4 )$ , $B = ( - 2,4 )$ ,and $C = ( - 3 , - 4 )$ .Round answer to two decimal places.

(Multiple Choice)

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Question 32

The vector $\mathbf { u } = \langle 2500,3000 \rangle$ gives the number of units of two models of laptops produced by a company.The vector $\mathbf { v } = \langle 2000,1000 \rangle$ gives the prices (in dollars)of the two models of laptops,respectively.Use dot products to determine the revenue for these two laptops if the price of each is increased by 3.5%.

(Multiple Choice)

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Question 33

Use the vectors $\mathbf { u } = \langle 3,5 \rangle$ , $\mathbf { v } = \langle - 2,4 \rangle$ ,and $\mathbf { w } = \langle 3 , - 4 \rangle$ to find the indicated quantity.State whether the result is a vector or a scalar. $\left( \mathbf { v } ^ \mathbf{ . } \mathbf { u } \right) \mathbf { w }$

(Multiple Choice)

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Question 34

The vector $\mathbf { u } = \langle 2700,4700 \rangle$ gives the number of units of two models of laptops produced by a company.The vector $\mathbf { v } = \langle 1200,900 \rangle$ gives the prices (in dollars)of the two models of laptops,respectively.Use dot products to determine the revenue for these two laptops if the price of each is increased by 6%.

(Multiple Choice)

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Question 35

Use the dot product to find the magnitude of u. $\mathbf { u } = \langle - 7,12 \rangle$

(Multiple Choice)

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Question 36

Given $\mathbf { u } = \langle - 5 , - 6 \rangle$ and $\mathbf { v } = \langle - 6 , - 5 \rangle$ ,find $u^.v$ .

(Multiple Choice)

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Question 37

Determine the work done by a person lifting a 240-newton bag of sugar 2 meters.

(Multiple Choice)

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Question 38

Find the projection of u onto v. =\langle3,6\rangle =\langle4,6\rangle

(Multiple Choice)

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Question 39

Find the dot product of u and v. =6+4 =8-2

(Multiple Choice)

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Question 40

Exam 39:Vectors and Dot Products

Find the angle θ\thetaθ between the vectors.​ =\langle4,0\rangle =\langle0,-3\rangle ​ (Round the answer to 1 decimal place. ) ​

Find the projection of u onto v if u=⟨4,−5⟩\mathbf { u } = \langle 4 , - 5 \rangleu=⟨4,−5⟩ , v=⟨3,−1⟩\mathbf { v } = \langle 3 , - 1 \ranglev=⟨3,−1⟩

Use the dot product to find the magnitude of u.​ u=35i+40j\mathbf { u } = 35 \mathbf { i } + 40 \mathbf { j }u=35i+40j ​

Find the dot product of u and v.​ =\langle5,1\rangle =\langle-2,4\rangle ​

Given u=−i+3j\mathbf { u } = - \mathbf { i } + 3 \mathbf { j }u=−i+3j and v=5i+4j\mathbf { v } = 5 \mathbf { i } + 4 \mathbf { j }v=5i+4j ,find u.vu^.vu.v

Find the dot product of u and v.​ =\langle-4,9\rangle =\langle-2,-5\rangle ​

Find the dot product of u and v.​ =\langle6,14\rangle =\langle-2,2\rangle ​

Use the dot product to find the magnitude of u.​ u=4j\mathbf { u } = 4 \mathbf { j }u=4j ​

Use vectors to find the measure of the angle at vertex B of triangle ABC,when A=(5,4)A = ( 5,4 )A=(5,4) , B=(−2,4)B = ( - 2,4 )B=(−2,4) ,and C=(−3,−4)C = ( - 3 , - 4 )C=(−3,−4) .Round answer to two decimal places.

Use the dot product to find the magnitude of u. ​​ u=⟨−7,12⟩\mathbf { u } = \langle - 7,12 \rangleu=⟨−7,12⟩ ​

Given u=⟨−5,−6⟩\mathbf { u } = \langle - 5 , - 6 \rangleu=⟨−5,−6⟩ and v=⟨−6,−5⟩\mathbf { v } = \langle - 6 , - 5 \ranglev=⟨−6,−5⟩ ,find u.vu^.vu.v .

Determine the work done by a person lifting a 240-newton bag of sugar 2 meters.

Find the projection of u onto v.​ =\langle3,6\rangle =\langle4,6\rangle ​

Find the dot product of u and v.​ =6+4 =8-2 ​

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Functions

Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Combinations of Functions Composite Functions

Inverse Functions

Mathematical Modeling and Variation

Quadratic Functions and Models

Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Complex Numbers

Zeros of Polynomial Functions

Rational Functions

Nonlinear Inequalities

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

Exponential and Logarithmic Models

Radian and Degree Measure

Trigonometric Functions The Unit Circle

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Inverse Trigonometric Functions

Applications and Models

Using Fundamental Identities

Verifying Trigonometric Equations

Solving Trigonometric Equations

Sum and Difference Formulas

Multiple Angle and Product to Sum Formulas

Law of Sines

Law of Cosines

Vectors in the Plane

Trigonometric Form of a Complex Number

Linear and Nonlinear Systems of Equations

Two Variable Linear Systems

Multivariable Linear Systems

Partial Fractions

Systems of Inequalities

Linear Programming

Matrices and Systems of Equations

Operations With Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

Sequences and Series

Arithmetic Sequences and Partial Sums

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Counting Principles

Probability

Lines

Introduction to Conics Parabolas

Ellipses

Hyperbolas

Rotation of Conics

Parametric Equations

Polar Coordinates

Polar Equations of Conics

Find the angle $\theta$ between the vectors. =\langle4,0\rangle =\langle0,-3\rangle (Round the answer to 1 decimal place. )

Find the projection of u onto v if $\mathbf { u } = \langle 4 , - 5 \rangle$ , $\mathbf { v } = \langle 3 , - 1 \rangle$

Use the dot product to find the magnitude of u. $\mathbf { u } = 35 \mathbf { i } + 40 \mathbf { j }$

Find the dot product of u and v. =\langle5,1\rangle =\langle-2,4\rangle

Given $\mathbf { u } = - \mathbf { i } + 3 \mathbf { j }$ and $\mathbf { v } = 5 \mathbf { i } + 4 \mathbf { j }$ ,find $u^.v$

Find the dot product of u and v. =\langle-4,9\rangle =\langle-2,-5\rangle

Find the dot product of u and v. =\langle6,14\rangle =\langle-2,2\rangle

Use the dot product to find the magnitude of u. $\mathbf { u } = 4 \mathbf { j }$

Use vectors to find the measure of the angle at vertex B of triangle ABC,when $A = ( 5,4 )$ , $B = ( - 2,4 )$ ,and $C = ( - 3 , - 4 )$ .Round answer to two decimal places.

Use the dot product to find the magnitude of u. $\mathbf { u } = \langle - 7,12 \rangle$

Given $\mathbf { u } = \langle - 5 , - 6 \rangle$ and $\mathbf { v } = \langle - 6 , - 5 \rangle$ ,find $u^.v$ .

Find the projection of u onto v. =\langle3,6\rangle =\langle4,6\rangle

Find the dot product of u and v. =6+4 =8-2