# Area of triangle using vector products.

#### scofield131

I'm only posting to have my answer checked, as I couldn't find a worked example or solution to explain how to solve this question in my notes and had to google it, which meant I could have done it completely wrong.

Three points in 3-space are given by A = (2, 1, 0), B = (5, 1, -1) and C = (-2, 0, 2). Calculate the area of the triangle (you may first calculate the vector products of AB and AC)

AB = [3, 0, 1] AC= [-4, -1, 0]

AB x AC = [-1, 1, 3]

A = 1/2 ( |AB x AC| )

1/2 (sqroot(11)) = 1.65

#### earboth

MHF Hall of Honor
I'm only posting to have my answer checked, as I couldn't find a worked example or solution to explain how to solve this question in my notes and had to google it, which meant I could have done it completely wrong.

Three points in 3-space are given by A = (2, 1, 0), B = (5, 1, -1) and C = (-2, 0, 2). Calculate the area of the triangle (you may first calculate the vector products of AB and AC)

AB = [3, 0, 1] AC= [-4, -1, 0] <<<<<<< these vectors are wrong

$$\displaystyle \overrightarrow{AB}=\vec b - \vec a = (3,0,-1)$$

AB x AC = [-1, 1, 3]

A = 1/2 ( |AB x AC| )

1/2 (sqroot(11)) = 1.65
...

scofield131