Question

Let u = <-4, -3>. Find the unit vector in the direction of u, and write your answer in component form.

Answer 1

@amistre64

Answer 2

unit is a term that means 1

spose we have a length of rope that is 23 feet long; how long is one unit?

Answer 3

1 foot

Answer 4

good, and we can verify that because 23/23 = 1

if a tree is 3 meters tall, how tall is one unit?

Answer 5

100cm

Answer 6

maybe ...

so how long is our vector?

Answer 7

1 unit

Answer 8

not quite

4^2 + 3^2 is not 1^2

graphically a vector represents the hypotenuse of a right triangle of sides x and y

Answer 9

so 5 units

Answer 10

if its 5 units long, then what do we scale it by to get a vector that is a unit long?

Answer 11

if something is 23 feet long, we divde it by 23
if something is 3 meters tall we divide it by 3

if something has a magnitude of K, then we divide it by K

Answer 12

a 1/5 scale or 1:5

Answer 13

... shoulda used L to keep it conformed to the drawing eh

Answer 14

correct

so we know u is already in a direction; we simply need to divide it by 1/5 to get its unit vector equivalent

Answer 15

\[\frac15<-4,-3>~or~<\frac{-4}{5},\frac{-3}{5}>\]

Answer 16

alright, thanks! I have one more related to the same section but not entirely the same

Answer 17

This always confuses me, even when I go step by step using the book:

Two forces with magnitudes of 100 and 50 pounds act on an object at angles of 50° and 160° respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer.

Answer 18

your adding vectors

translating the end result tho gets triggy

show me what your process is so far

Answer 19

one sec

Answer 20

I can't figure it out right now. I've been logged off of my class and can't get back on. Can you help me get started so I can do it by hand?

Answer 21

we have 2 vectors whose x and y parts need to expressed in cos and sin of the angles

100(x1,y1) + 50(x2,y2)

100(cos(50), sin(50)) + 50(cos(160),sin(160))

100cos(50) +100sin(50)
50cos(160) +50sin(160)
---------------------
X Y

we get the resulting vector (X,Y)

determine its length sqrt(X^2+Y^2)

then comes the triggy part: tangent uses Y/X soo

tan(a) = Y/X

a = inverse tan(Y/X)

Answer 22

So we need the length first?

Answer 23

not really, the length is just asked for, otherwise (X,Y) is a vector sufficient for the cause. but its asking for the properties of the vector so we have to dissect it

Answer 24

have you determined the (X,Y) parts yet?

Answer 25

Sorry had to talk to my dad real quick. Working on it now

Answer 26

So the vector would be (100cos(50) +100sin(50), 50cos(160) +50sin(160)) right? Just have to simplify it

Answer 27

like parts .... add like parts

cos to cos and sin to sin

Answer 28

So would sin be x and cos be y?

Answer 29

or cos is x and sin is y?

Answer 30

well that was a 50/50 i spose

no, x is by convention a cosine measure, and y is a sin measure.

Answer 31

Ok so x would be 17.29?

Answer 32

x=17.2941 is what i rnded to so i agree there