Question

@vocaloid

Answer 1

@Vocaloid

Answer 2

Post your question.

Answer 3

@Shadow

Answer 4

\(\sf <x_2-x_1,y_2-y_1>\)

Answer 5

Given the start and end points in the form of (x1, y1), (x2, y2).

Answer 6

What is the start and end point of vector v?

Answer 7

-2,3
4,4

Answer 8

Yep, now plug them into here:

\(\sf <x_2-x_1,y_2-y_1>\)

Can you do that?

Answer 9

6,1 so c

Answer 10

@igreen

Answer 11

@Vocaloid

Answer 12

kind of need to do trial and error on this one, go one by one and calculate terminal - initial and see which one gives a magnitude of 17

Answer 13

magnitude is term-initial then square and root it right?

Answer 14

yeah sort of, you'd subtract terminal - intial, then calculate r = sqrt(x^2 + y^2) based on the difference

Answer 15

that was easy a lol

Answer 16

good

Answer 17

tip to tail method, re-draw the tip of one arrow at the tail of the other arrow (probably easier to draw than describe)

Answer 18

then you draw an arrow from the tail of v to the tip of u like so:

Answer 19

is 3 a this type question I got wrong last time lol

Answer 20

it's kind of hard to see, but since the final arrow is pointing up and to the right, which answer do you think might look the best?

as a hint: you are adding two vectors so the final answer must also be a vector

Answer 21

for a vector pointing up and to the right, would you expect the coordinates to be positive or negative?

Answer 22

imagine a vector at (0,0) pointing up and towards the right

Answer 23

notice how the vector is pointing up along both axes so we would naturally expect the coordinates to be positive

making <7,6> the only viable answer that is a vector w/ positive coordinates

Answer 24

for 4) you just need to subtract terminal - initial, then apply the transformation -2AB bby multiplying AB by -2

Answer 25

I'm back sorry was busy with something

Answer 26

so b

Answer 27

for 4, yeah, I got B too

Answer 28

3 and 4 are actually both B

Answer 29

yes I saw ;

Answer 30

for 3) first find 2u by multiplying 2 by u, then find 4w using the same logic/reasoning, then finally subtract 2u - 4w based on your results from the earlier steps

Answer 31

since all of the x-coordinates are different you only need to consider the first coordinate of each vector

Answer 32

b? hold on I'm rechecking

Answer 33

just check the first coordinates of each vector

2u - 4w --> 2(-1) - 4(2) = ?

Answer 34

-10

Answer 35

so a

Answer 36

good, so if the first coordinate is -10 that eliminates all possibilities except a

Answer 37

for 6) the first coordinate goes in front of i and the second coordinate goes in front of j

so

-3i + 4j

Answer 38

for 7) you need to calculate v by taking terminal - initial, then calculate 2v - 3u

Answer 39

c?

Answer 40

i got something a little diff

what did you get as your vector v?

Answer 41

-12,2

Answer 42

good, so u = <-3,4) and v = <-12,2>

2v - 3u = 2<-12,2> - 3<-3,4> = ?

as a hint try to consider the x and y-coordinates separately then put them together into a final vector

Answer 43

-24,4
-9,12

Answer 44

I was trying to use u and terminal, too lol

Answer 45

good, so

-24 - (-9) = ?
4 - 12 = ?

then put 'em together

Answer 46

15
-8

Answer 47

careful with the first sign, it's -15

so A -15i - 8j

Answer 48

anyway for 8) calculate the magnitude of the vector first, then find the unit vector by dividing vector/magnitude

Answer 49

right and hold on

Answer 50

b

Answer 51

you're close, you should have gotten sqrt(13) as the magnitude, when you divide -3/sqrt(13) then rationalize it you get -3sqrt(13)/13 not -3sqrt(13)/5 so A not B

Answer 52

@Vocaloid

Answer 53

1) tan(theta) = y/x

plug in y and x and solve for theta, you'll need a calculator for this wolfralpha.com

Answer 54

a?

Answer 55

good

for 2) let's try sketching the given angle and magnitude

Answer 56

any ideas how you would calculate the height/length of that triangle?

Answer 57

by using sohcahtoa or something like that

Answer 58

yeah, there's a bit faster method though b/c this is a 30-60-90 triangle

the side across from the 30-angle is half the hypotenuse so:

Answer 59

making B the only possibility since it starts w/ -2.5

Answer 60

similar thing w/ problem 3, sketch the triangle like so:

Answer 61

oh cool

Answer 62

this is another 30-60-90 triangle, try calculating the height and length of the triangle to figure out the coordinates of the vector

Answer 63

good, D is right

Answer 64

it is oh ok then d

Answer 65

and now #4

Answer 66

huh I don't exactly remember but I think we would start with resolving the two vectors into their cos/sin components

so 175cos(40) + 35cos(60) gives the x-coordinate I think and
175sin(40) + 35sin(60) should give the y-coordinate, then you'd calculate the magnitude of the new vector

Answer 67

so i have 151.5 and 142 so far

Answer 68

good so <151.5, 142> is the new vector, calculate the magnitude and direction

remember the angle is given by tan(theta) = y/x and the magnitude is r = sqrt(x^2 + y^2)

Answer 69

c

Answer 70

awesome

Answer 71

1. tan(theta) = y/x solve for theta

Answer 72

b?

Answer 73

awesome

for 2) <magnitude*cos(theta), magnitude*sin(theta)> = ?

Answer 74

a

Answer 75

other way around, switch the coordinates, so C

Answer 76

3) same thing, magnitude*cos(theta), magnitude*sin(theta)

Answer 77

d

Answer 78

good

Answer 79

similar as the airplane problem, first find

magnitude*cos(theta) + other magnitude*cos(other theta) = the new x-coordinate

then find

magnitude*sin(theta) + other magnitude*sin(other theta) = the new y--cordinate

put those in a vector then find the direction/magnitude

Answer 80

ship: magnitude 22, theta = 157 degrees
current: magnitude 5, theta = 213

calculate the new x and y component of the vector

Answer 81

I have -12 now what would the magnitude to divide by is

Answer 82

your vector needs to have an x and y- coordinate

Answer 83

ok so -24 and 12

Answer 84

current magnitude*cos(theta) + ship magnitude*cos(theta) = ?

Answer 85

check your calculations again

Answer 86

a?

Answer 87

good, A

it's 1AM, I need to go to sleep

Answer 88

okay goodnight