Question

hi every one :) ,
i have a question about lec 19
the forth example about vector field
i think the vector should have been in the forth quarter of the plane
:)

Answer 1

can you be more explicit? what example and what is your question about it?

Answer 2

THIS SPOT MIN 11:41

Answer 3

if you are at (x0,y0) and use the "rule" (-y0, x0)
the new point is rotated counter-clockwise around the origin by 90 degrees.

perhaps if we take a few examples:
(1,0) becomes (-0,1) or just (0,1).
(2,1) becomes (-1, 2) (this is the second quadrant)

to rotate clockwise we would use this rule:
(x,y) -> (y,-x)

and (2,1) --> (1, -2)

Answer 4

the demanded coordinates is ( -y,x) not (y,-x)
according to the question
the vector is
F=xi + -yj

Answer 5

The field is defined as
\[ \vec{F} = -y \hat{i} + x \hat{j}\]
Denis is showing how to find the field at a point (x,y)

He did this by saying that the vector \( -y \hat{i} + x \hat{j} \) can be represented as the vector from the origin to the point (x,y) that is then rotated 90 degrees counter-clockwise to the point (-y,x).

At point (x,y) we visualize a vector in the direction (-y,x) with length \(\sqrt{x^2+y^2}\)

Answer 6

**At point (x,y) we visualize a vector in the direction from (0,0) to (-y,x)....

Answer 7

The point (x,y) can be any where (any quadrant).

If it were at (-1,+2) for example, the field at that point will be
\( -2 \hat{i} - \hat{j} \)

Answer 8

got it sir thanks :)