Question

Let u = <-8, -9>. Find 7u.
<-56, 63>

<-56, -63>

<56, -63>

<56, 63>
I feel like its the second one but im not sure...can someone explain this concept please:)?

Answer 1

correct, you multiply each component by 7

Answer 2

ok so if there was a question that said, Let u = <7, -3>, v = <-9, 5>. Find 4u - 3v, do I just distribute the number to each corresponding variable?

Answer 3

it's technically not distribution, but you can think of it like that

Answer 4

distribute is not the correct term .... oh so my proffessor told me when i stated the same thing :)

Answer 5

what do you get when you compute 4u ?

Answer 6

one minute im gonna try solving this:p

Answer 7

ok well I got 4u = <28, -12> and 3v as <-27,15>...where do I go from there?

Answer 8

spose we take a u = (a,b)

this can be represented in component form as u = ai + bj

u+u+u+...+u (k times) is therefore

ai + bj
+ai + bj
+ai + bj
+ ...
+ai + bj
--------
(a+a+a+...+a)i
+(b+b+b+...+b)j

which of course is just kai + kbj = k(ai + bj) or k(a,b)

Answer 9

now you add up the vectors

Answer 10

add the corresponding components

Answer 11

when you say add up the components, would you get <55,-27>?

Answer 12

add as in combine like parts ...

28 and -27 combine to 1

Answer 13

-12 and 15 combine to ??

Answer 14

(a,b) + (x,y) = [(a+x) , (b+y)]

Answer 15

but doesn't 28-(-27)=55?
and -12-15=-27?
because the question I am solving is 4u-3v

Answer 16

hmm, foiled by a horizontal construction again ...

Answer 17

your right

Answer 18

oh right, 4u - 3v not 4u + 3v

Answer 19

4u = <28, -12>
-3v = -<-27,15>


4u = <28, -12>
-3v = <27,-15>

youre fine

Answer 20

lol just wanted to make sure:) are u willing to help me with a few more questions?

Answer 21

as long as your willing to correct the mistakes ;)

Answer 22

haha ok:) ok here is the next question that I just don't get at all...
Let u = <-4, -3>. Find the unit vector in the direction of u, and write your answer in component form.

Answer 23

think of vectors as right triangles ...

Answer 24

ok

Answer 25

when we want a unit vector, we want it to be of length 1, divide it all by r

Answer 26

the unit vector of u is just u divded by its own length

Answer 27

u = <-4, -3> this is the obiquitous 3,4,5 triangle r = 5

unit u = 1/5 <-4,-3>

Answer 28

so it would be < (-4/5),(-3/5)>?

Answer 29

thatll work too

Answer 30

ok two more questions:)
Given that P = (2, 9) and Q = (4, 14), find the component form and magnitude of PQ->

Answer 31

well, if P was at the origin, the we could just read the vector off of Q right?

Answer 32

subtract P from both points

Answer 33

?? sorry im just getting really confused on this question. we have been doing something similar in physics and idk the actual concept of vectors

Answer 34

a vector is graphically an arrow

Answer 35

ok...so when u say to subtract point p, is the answer <2,5>? and how do you find the magnitude?

Answer 36

to find the arrow from P to Q, its the same arrow as from P-P to Q-P