Question

Help with Vectors question?



a) Does u x v = v x u (Both u's and v's have direction arrows over them)? Explain and illustrate with a diagram.

b) Explain why it is not possible for a line in 3 space to be represented by a scalar equation.

All help is appreciated :)

Answer 1

i assume a is a dotproduct, and dots are commutative

Answer 2

x,y
a,b
-----
ax+by


a,b
x,y
-------
ax+by

same same

Answer 3

b looks more like someone trying to get you to conform to a singular view of things .... so i wouldnt know what they are talking about in that ont

Answer 4

word^
not sure how a diagram helps much for part a either

Answer 5

might be a british thing :)

Answer 6

Oh, im sorry lol, I solved it (actually textboom did :P)
A line in 3 space can also be defined by a vector equation or by parametric equations. It cannot, however, be defined by a scalar equation. In 3 space, a scalar equation defines a plane, A plane is a 2 dimensional flat surface that extends infinitely far in all directions.

Answer 7

**textbook

Answer 8

textboom sounds better, more hip and suave lol

Answer 9

LOL

Answer 10

That is the answer for part b), but I have no idea on how to do part a) :/

Answer 11

lol I thought OS was out of business for a sec
but that explanation doesn't reaslly say why you \(can't\) represent a line in 3space with scalars, just that you can represent a plane....
not an exclusive answer in my opinion

Answer 12

without a dot inbetween u and v on a, its hard to tell what they want

Answer 13

it literally says uxv=vxu

Answer 14

with arrows ofcourse

Answer 15

cross product, oh; then thats not communicable

Answer 16

\[(\vec u)\times(\vec v)\neq(\vec u) \cdot(\vec v)\]very important

Answer 17

when talking vectors, its assumed that your letters a vectors ...

Answer 18

\[\vec u\times\vec v=-(\vec v\times\vec u)\]I beleive

Answer 19

yes

Answer 20

you can show it with an example

Answer 21

u = 1,0,0
v = 0,1,0

cross them both ways and see

Answer 22

So, what should I do for part a)?

Answer 23

follow the directions :)

Answer 24

i know how to show that a cross is not commutative; but diagram it? dunno

Answer 25

Maybe thats how the question wants it? The question is straight out of my textbook :P

Answer 26

Its under the chapter: Equations of lines in two-space and three-space

Answer 27

look in the chapter to see an example of how a diagramed solution looks

Answer 28

all the stuff between homework problems is good reading at times ;)

Answer 29

mysite.science.uottawa.ca/vbozi013/mat1339/ch08.pdf I found the answer to part a) under chapter 8.1 and the question is on pg 438 #17

Answer 30

:/ I cant find any illustration

Answer 31

Don't know :S