# Thread: How to find area of triangle with two vertices?

1. ## How to find area of triangle with two vertices?

How do I find the area of a triangle with two sides given by a = <1,3,-1> and b = <2,-1,2>? Thank you.

2. Originally Posted by henrymath
How do I find the area of a triangle with two sides given by a = <1,3,-1> and b = <2,-1,2>? Thank you.
what does $|\vec{a} \times \vec{b}|$ get you?

3. Originally Posted by skeeter
what does $|\vec{a} \times \vec{b}|$ get you?
I get
a x b = 5i - 4j - 7k

4. Originally Posted by henrymath
I get
a x b = 5i - 4j - 7k
the magnitude of the cross product of two vectors is the area of the parallelogram formed with the two vectors as adjacent sides.

triangle area = 1/2 parallelogram area

5. Originally Posted by skeeter
the magnitude of the cross product of two vectors is the area of the parallelogram formed with the two vectors as adjacent sides.

triangle area = 1/2 parallelogram area
Thanks. my answer was 1/2 sqrt 90.