Question

Find the area of triangle with given vertices. (1/2)
||u x v||.

A(0,0,0), B(1,0,3), C(-3,2,0)

Answer 1

oh and this involves vectors

Answer 2

I've already gotten the correct answer, my only question is when you go about using the cross product, can I choose any vector combination AB x AC, BA x BC...etc.?

Answer 3

the cross of 2 vectors gives us a new vector; and the magnitude of that new vector is the "area" of the parallelpiped

Answer 4

you should be able to yes

Answer 5

since A is at 0, your B and C are vector components already

Answer 6

BxC = say N

|N| = area of the parallelagram; so half that is the triangle part

Answer 7

ok, cause I noticed that no matter which one I choose (AB x AC or BA x BC) the magnitude for both were the same.

Answer 8

x 1 -3 x = 0-6
y 0 2 -y = (0--9)
z 3 0 z = 2-0

<-6,-9, 2> ^2 = \(\sqrt{36+81+4}\)/2 for triangle area

Answer 9

they are all the same parts of the same triangle, so they should match up in the end

Answer 10

okay. Thanks.