Question

Calculate the area of the triangle with the given vertices: A(2, 0, 0), B (0, 2, 0) and C(0, 0,
2) ?

Answer 1

i figured out AB =(2,0,-2)
AC = (0,2,-2) & BC = (-2,2,0)

Answer 2

what to do from there?

Answer 3

AB x AC
You know vectors?

Answer 4

<2,-2,0>
<2,0,-2>

Answer 5

why do i cross product them?

Answer 6

It is a vector method of finding the area. What method are you attempting (1/2)bh

Answer 7

i was thinking of finding the absolute value of AB, AC, and BC for the length of each side

Answer 8

then doing something from there

Answer 9

so i can cross product any of the of length coordinates and get an area?

Answer 10

Cross sides AB and AC. And find the magnitude. That is the area of the related parallelogram; half that is the area of your triangle. The area is\[2 \sqrt{3}\]Try your method, see if you get the same thing.

Answer 11

kk

Answer 12

didnt get same answer but i never knew cross product was used to find area...ty

Answer 13

Let's see the work from your method.

Answer 14

What is this? 'i figured out AB =(2,0,-2) AC = (0,2,-2) & BC = (-2,2,0)' Is this the vector AB? and AC?

Answer 15

from there i got |AB|= |AC| = |BC| = 2sqrt(2)

Answer 16

oh i get the right answer

Answer 17

but had to assume it was a right angle triangle

Answer 18

with all the lengths and just assuming its a right angle triangle i figure out height: b^2=c^2-a^2 and plug everything in

Answer 19

but cross product is soo much faster

Answer 20

Powerful tool.