Question

Are standard basis vectors constant?

Answer 1

no, what do you mean

Answer 2

are vectors even important?

Answer 3

or better yet...is Math important?

Answer 4

In one of the examples, I noticed that they made a quick substitution for the following vectors:\[\overrightarrow{i} = \langle 0,0,1\rangle\]\[\overrightarrow{j} = \langle 0,1,0\rangle\]\[\overrightarrow k = \langle0,0,1\rangle\]So are vector i, vector j and vector k defined vectors?

Answer 5

im thinking these are \(\hat i, \; \hat j, \; \hat k\) for some reason

Answer 6

http://tutorial.math.lamar.edu/Classes/CalcII/VectorArithmetic.aspx
"Standard Basis Vectors Revisited"

Answer 7

i must be <1,0,0>

Answer 8

yes you are

Answer 9

Oh yes,\[\overrightarrow{i} = \langle1,0,0\rangle\]Sorry... messed up

Answer 10

still thinking that's supposed to be \(\hat i\)

Answer 11

OK, but is \(\hat{i}\) the same as \(\overrightarrow{i}\)?

Answer 12

\[\hat i = \; \text{positive x-axis}\]

Answer 13

no they are not

Answer 14

OK

Answer 15

and yes, i is defined as unit vector in x direction
j is defined as unit vector in y direction
k is defined as unit vector in z direction
and denoted by i^ as said by lg

Answer 16

\[\vec i \implies \text{vector}\]
\[\hat i \implies \text{vector component}\]

Answer 17

I don't really get any of those, but thanks :P

Answer 18

Yeah... @hartnn that's right!

Answer 19

think of it somehow like this:

i => x

j => y

k => z

Answer 20

Yeah, I do!

Answer 21

\[\vec\imath=\langle 1,0,0\rangle\]\[\vec\jmath=\langle 0,1,0\rangle\]\[\vec k=\langle 0,0,1\rangle\]

Answer 22

+ i => positive x-axis
-i => negative x-axis
+ j => positive y-axis
- j => negative y-axos
k => positive z axis
-k => negative z-axis

Answer 23

That's a nice way to handle it! :)

Answer 24

can u imagine a vector along x-direction and magnitude = 1.......thats i