Question

What does the scalar result of dotting 2 vectors signify? I know a 0 means they are perps, but what is the scalar product actually mean?

Answer 1

<1,1>.<0,2sqrt(2)> = 0 + 2sqrt(2) = 2sqrt(2).

That doesnt make sense to me a whole lot.

Answer 2

that just seems to give the magnitude of the bottom vector

Answer 3

<1,1>.<0,2sqrt(2)> = 0 + 2sqrt(2) = 2sqrt(2). how?

Answer 4

It gives the cosine of the angle between them. This is the way you can get angles in any vector space with an inner product.

Answer 5

<1 , 1 >
<0,2sqrt(2)>
------------
0 + 2sqrt(2) = 2sqrt(2)

Answer 6

yes, it gives the adjacent part of the cosine angle which is just the magnitude of the bottom vector right?

the product of the magnitudes of the top and bottom vectors account for the 'hypotenuse' then

Answer 7

<1 , 1 >
<0,2sqrt(2)>
------------
0 + 2sqrt(2) = 2sqrt(2). iam not geting it amistre

Answer 8

see; it is how you multiply vectors; or at least one way to do it; the other being the cross product

Answer 9

cross product can be found two ways if i remember correctly
finding the determinant of a matrix
or some kind of trig thing right?

Answer 10

determinate of 2 vectors is usual

Answer 11

the other way is just to equate the zero dot product of 2 vectors inthe plane and equat them

Answer 12

v<x,y>
n<a,b>
-------
vx.a + vy.b = 0

u<x,y>
n<a,b>
--------
ux.a +uy.b = 0

equate them and solve the system of equations :)

Answer 13

geterminate is mor emechanical tho

Answer 14

lol... read thru the typos

Answer 15

i now the scalar projection projects the top onto the bottom at |top|cos(a)

Answer 16

i just dont understand if there is another way to use the scalar product other than associating it to the cos(a) between the 2 vectors :)

Answer 17

example: find u*v if u=2i+3j and v=-2k

| i j k | = i|3 0 | -j|2 0| +k|2 3| =i(-2(3)-0)-j(-2-0)+k(0-0)=-6i+2j
| 2 3 0 | |0 -2| |0 -2| |0 0|
| 0 0 -2|

Answer 18

correct; just keep in mind to do +-+ :) that middle - is to account for being lazy i think lol

Answer 19

=-6j+4k

Answer 20

oops
=-6i+4j

Answer 21

i forgot about that othr two up there

Answer 22

2a+3b+0c = 0

0a+0b-2c = 0

lol... thats would be hard to determine that way ; cross product is better in that case; and in most cases prolly

Answer 23

yes that would be hard lol (or impossible) i dont see how we could do it that way