Question

I cannot get the format right for the vectors, sorry:

Suppose "underscore" u = (u1, u2, u3)

Is this true?
"underscore" u "dot" u = sqrt(u1^2 + u2^2 + u3^2

Please explain in detail, thanks

Answer 1

try it out.

Answer 2

<a,b,c>.<x,y,z> = ax + by + cz right?

Answer 3

ok.....

Answer 4

whats an underscore u?

Answer 5

like i said, can't get the format right sorry. I'm referring to a vector. I have a solution but i dont understand it, will try and post it now

Answer 6

since we are taking vectors, itll be assumed that u is a vector

Answer 7

perhaps the notation: u = <u1,u2,u3> might make life simpler

Answer 8

i have a meeting starting soon, so ill check in on this in about an hour to see if anyones gotten back to you

Answer 9

I've attached, thanks.

Answer 10

I have more questions on vectors and de moivre's theorem. Will mail it to you if you don' t mind. Thanks

Answer 11

i notice that the underscore is your materials way of expressing a vector then. Alot of texts boldface it or put an arrow above it, but all that is for is trying to come up with a suitable means of getting a point across.

the dot product is an operation on vectors that is related to multiplication, except for in R^2 instead of R^1

a vector of R^1 would just look like a number, an ordered pair with a single element,

u = 3 would be a vector from the origin to the point x=3.
v = -2 would be a vector from the origin to the point x=-2

u.v is defined the same way as other dimensional ordered pairs, but since there is no other element in the setup, its just multiplication of like elements,

u = 3
v = -2
--------
u.v = -6


When we lift this into higher dimensions, we have the same concepts, but after we multiply like elements, we add up all the results. say:

u = < 3,5>
v = <-2,2>
------------
u.v = -6+10 = 4

Answer 12

Hi, thanks so much for your explanation. It is much appreciated.