Question

A triangle has vertices A (-2, 1, 3). B (7,8,-4,) and C(5,0,2). find the area.

Answer 1

Familiar with the vector product?

Answer 2

I found the magnitude of AB then the magnitude of AC, and used the cross product and got [-14,-40, -58]

Answer 3

but what do i do here? area of triangl is bh/ 2 so do i divide this by 2 ?? and then used pythagorean theorem

Answer 4

Oh right pardon me, in your tongue it's cross product *grins*

\[\Large \vec{a}\times\vec{b}=\vec{n} \]
That is a vector again, hence I call it usually vector product, you need to find the magnitude of that vector \(\vec{n}\), when you've done that, that gives you the area of the parallelogram.

So divide that by two, as you suggested.

Answer 5

you don't need the magnitude of AB and AC individually, just the magnitude of \(\vec{n}\)

Answer 6

ok so a parallelogram is 2 triangles then i divide the area by 2

Answer 7

exactly

Answer 8

thank you , i got the answer !

Answer 9

you're welcome