Question

Is it possible to use the dot product with a vector and magnitude? ie. r dot |r|

Answer 1

no

Answer 2

do you just distribute?

Answer 3

yes

Answer 4

no, because x dot y is defined only when x and y are both vectors

Answer 5

a vector times a scalar is distribution

Answer 6

right but a vector dot scalar is distribution?

Answer 7

If the vector x = <a, b> and | x | = c for some scalar c, then

|x|*x = c*<a,b> = <ca, cb>

Answer 8

so what would be the outcome of r dot r'(0)???

trying to figure out what r is because i know i have the right answer but this program we use says it isn't

Answer 9

ahhhh so you can then

Answer 10

r looks like a function in polar coordinates

Answer 11

or it's probably just an ordinary vector function

Answer 12

it's r(t) = <7x, sqrt(39-49x^2)> Find r dot r'(0)

Answer 13

ok

Answer 14

so r'(t) = derivative of r(t)

Answer 15

but that can't be tho... cuz the answer would be 49x... which it wont accept

Answer 16

yeah

Answer 17

so derive each component

Answer 18

-49x / 2 sqrt ( 39 - 49x^2)

Answer 19

to get r'(t) = <7, (-49*x)/sqrt(39-49*x^2) >

Answer 20

but it doesn't really matter tho bc you do r'(0), which makes the y component = 0

Answer 21

u are missing a 1/2 in the y component, but yeah that's what i got

Answer 22

So r'(0) = <7, 0 >

Answer 23

the 2's cancel

Answer 24

yeah, then <7,0> dot <7x, sqrt(39 - 49x^2> right?

Answer 25

yep

Answer 26

which would come out 49x

Answer 27

the program says invalid answer format when i plug that in

Answer 28

are you sure it's r'(0)?

Answer 29

seems too easy to be zero

Answer 30

positive

Answer 31

can you take a screenshot of the problem?

Answer 32

yeah, it litterally says r dot r'(0)

Answer 33

sure 1 sec

Answer 34

shouldn't it say r(t) dot r'(0) tho? er i guess that doesn't matter

Answer 35

grrr i hate these stupid online programs that they make us use. The problems are so simple, yet you have to waste sooo much time trying to use the program

Answer 36

was thinking maaaybe the r meant magnitude? it kinda works out

Answer 37

t's cancel out and you are left with 39

Answer 38

yeah idk, programming error i guess

Answer 39

not sure if you multiply or add from there tho

Answer 40

eh 3 tries, gonna try it

Answer 41

faaack

Answer 42

it's odd how they refer to it as r dot r'(0) and not r(t) dot r'(0)

Answer 43

yeah that's what i was thinking. bc there are other problems where they say r(t)

Answer 44

does it give you any hints?

Answer 45

maybe they're thinking of the unit vector?

Answer 46

no hints available

Answer 47

eh no way tho, why would they leave it up to interpretation

Answer 48

idk

Answer 49

you'll just have to take it up with your teacher

Answer 50

because that is the right answer

Answer 51

yeah, no good. Alright, well thanks for the help. i do appreciate it

Answer 52

k np