Basic Operations of Vectors

​6.6 Vectors

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A vector can be multiplied by a real number called a ____________. (use all lower case letters) #42

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The sum of vectors v and w is represented by v+w. This is known as the _____________ vector. (use all lowercase letters) #43

Multiple Choice

Find the component form of vector AB with initial point A(0, 8) and terminal point B(-9, -3). #3

• <-9, 5>

• <-9, 11>

• <-9, -11>

• <-9, 5>

Multiple Choice

A vector is a mathematical structure that has both _______ and _______. #7

• direction, magnitude

• scope, sequence

• meat, potatoes

• scalar, vector

Multiple Choice

What is the horizontal component of $$v=<v_1,v_2>$$  ? #18

• $$v_1$$  

• $$v_2$$  

• none of these

Multiple Choice

What is the vertical component of $$v=<v_1,v_2>$$  ? #17

• $$v_1$$  

• $$v_2$$  

• none of these

Multiple Choice

Write $$v=<v_1,\ v_2>$$   as a linear combination of i and j. #20

• $$v_1\ +\ v_2$$  

• $$v_1i\ +\ v_2i$$  

• $$v_1i\ +\ v_2j$$  

• $$v_1j\ +\ v_2i$$  

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Multiple Choice

Find the magnitude of the vector <2, -3>. #8

• √11

• 13

• √-4

• √13

Multiple Choice

Find the magnitude of vector AB if the initial point is (-3, 1) and the terminal point is (3, 9). #2

• 6

• 8.2

• 10

• 10.4

Multiple Choice

Find the magnitude of the vector <10, -8>. #35

• 2

• 12.81

• 6

• 18

Multiple Choice

Find the dot product:   $$v\cdot w$$  .  v=2i + 3j and w=7i - 4j. #1

• 14i - 12j

• 5i - 7j

• 2

• -2

Multiple Choice

Find the dot product of <1, -2> and <3, 2>. #9

• 1

• <3, -4>

• <4, 0>

• -1

Multiple Choice

Find the angle between vectors <1,3> and <2,-5>. #10

• 40.24°

• 49.76°

• 139.76°

• 92.57°

Multiple Choice

Find the angle between u and v. #12

• 78.930^o

• 33.691^o

• 101.070^o

• 146.310^o

Multiple Choice

Find the unit vector in the direction of v = <-3,3>. #15

• <-3,3>

• $$<\frac{-1}{3\sqrt[]{2}},\frac{1}{3\sqrt[]{2}}>$$  

• <-3/18, 3/18>

• $$<\frac{-1}{\sqrt[]{2}},\frac{1}{\sqrt[]{2}}>$$  

Multiple Choice

Find the unit vector in the direction of v = <5,12>. #16

• <5,12>

• $$<\frac{5}{13},\frac{12}{13}>$$  

• $$<\frac{5}{\sqrt[]{13}},\frac{12}{\sqrt[]{13}}>$$  

• $$<\frac{5}{\sqrt[]{2}},\frac{12}{\sqrt[]{2}}>$$  

Multiple Choice

If w = <2, -5> and y = <2, 0>, find 2w + y. #4

• <-10, 2>

• <4, -5>

• <-6, 10>

• <6, -10>

Multiple Choice

Given u = <3, 7> and v =<-5, 4>, find 2v - 3u. #6

• <21, 2>

• <-19, -13>

• <-15, 3>

• 23

Multiple Choice

If vector A has an x component of 12 units and a y component of 7 units, what is the magnitude of vector A? #32

• 19 units

• 13 units

• 14 units

• 193 units

Multiple Choice

Remember, do a diagram if you think it will help:

A body is acted on by a vertical force of 18 N and a horizontal force of 32 N.

The angle to the horizontal of the resultant force is given by #33

• $$\cos^{-1}\left(\frac{18}{32}\right)$$

• $$\tan^{-1}\left(\frac{18}{32}\right)$$

• $$\sin^{-1}\left(\frac{32}{18}\right)$$

• $$\tan^{-1}\left(\frac{32}{18}\right)$$

Multiple Choice

Find the magnitude of the resulting force of the combined vectors given their magnitude and direction: F₁ : magnitude = 60 lbs, θ = 80° F₂ : magnitude = 80 lbs, θ = 20° #37

• 121.66 lbs

• <85.6, 86.5>

• 45.3°

• 140 lbs