Question

Another vectors Q

Answer 1

Can someone please explain this? What do the e1 and e2 mean?

Answer 2

e1 is another name for the vector (1,0). This vector points directly east
e2 is another name for the vector (0,1). This vector points directly north

if you wrote 2*e1, then you move 2 units east
if you wrote 3*e2, then you move 3 units north

combine the two to write 2*e1+3*e2 and that means you go 2 units east then 3 units north

Answer 3

The vector (-2,5) can be written as -2*e1+5*e2

that means you start at the origin, then you go 2 units west (to the left) and then 5 units north (up). So you'd go from the point (0,0) to the point (-2,5)

Answer 4

Why don't they use \( i \) and \( j \) like normal people.

Answer 5

e1 is probably better because i = sqrt(-1) is usually more common

\[\Large \vec{i} = \vec{e_1} = <1,0>\]
\[\Large \vec{j} = \vec{e_2} = <0,1>\]
Also, I think angle brackets are more suited for vectors than parenthesis are. Just to avoid confusion with ordered pairs.

Answer 6

Eh, I feel like context makes it clear, or the little hat thingies on top of the vector i, to distinguish from the imaginary unit.

Answer 7

I've never seen e1 and e2 before today.

Answer 8

notation like that is common in linear algebra when it comes to dealing with basis matrices

so that may be part of the motivation to use it

Answer 9

I took some linear algebra in university.. but maybe i just forgot about ever seeing this notation.

Answer 10

Do you understand @Abbles?

Answer 11

Yes! Thank you both :)
e1 is east, -e1 is west, e2 is north, -e2 is south.
They didn't even mention that in the course.. -_-

Answer 12

One thing I should clarify is that e1 is 1 unit east and e2 is 1 unit north

but yes, you have the right ideas @Abbles

Answer 13

@Abbles they probably don't because it's in terms of x and y, not NESW.

Answer 14

^That makes sense. They still could have explained it better...
but that's what open study is for :)

Answer 15

:)