Question

The area vector of a flat, oriented surface is a vector A such that the magnitude of vector A is the area of the surface.
Why is this so????

Answer 1

I dont understand y and its bothering me

Answer 2

In vector algebra, the cross product of two vectors aXb produces a vector orthogonal to a and b with magnitude equal to the area of the quadrilateral implied by a and b.

In geometric algebra then the "area vector" (??) would be a bivector.

Answer 3

wait i am just reading it

Answer 4

what is a bivector? and i am confused cuz like I am working with the dot product here not the cross product

Answer 5

Ok, forget bivector (this is geometric algebra, an alternative to vector algebra).

Draw a and b with angle theta between then dotting gives the projection of a on b via a cos theta.

Whereas a sin theta would give you the height and therefore the area of the quadrilateral.

Is that what you mean?

Answer 6

Obviously I am talking about the magnitudes here....

Answer 7

hahah i will have to reread it a few times. I need to brush up my vector algebra Thanks

Answer 8

Also aX(bXc) = b(a dot c) - c(a dot b) if that is any help.

I am not really sure whay u mean by "area vector".

Answer 9

neither do i lol. Thanks estudier :)

Answer 10

u r welcome:-)