1. ## Area of Triangle

Hey,

Im having trouble with these two questions, im getting stuck when im multiplying AB x AC

Thanks

2. Originally Posted by mikel03
Hey,

Im having trouble with these two questions, im getting stuck when im multiplying AB x AC

Thanks
I'm not sure what you mean by multiplying.... do you mean the cross product?

If so

First we need to create two vectors that are sides of the triangle

Using the head - tail method

if A and B will the heads and C the tail so we get

$\displaystyle (1,2,3)-(3,4,5)=(-2,-2,-2)$ ad

$\displaystyle (-1,5,-1)-(3,4,5)=(-4,1,-6)$

Now we want half of the magnitude of the cross product and that will be the area of the triangle.

$\displaystyle \begin{vmatrix} \vec i & \vec j & \vec k\\ -2 & -2 & -2 \\ -4 & 1& -6 \\ \end{vmatrix}=(12+2)\vec i-(12-8)\vec j+(-2-8)\vec k = 14 \vec i -4 \vec j -10 \vec k$

Now we just take half of the magnitude of this vector and we are done

$\displaystyle \frac{1}{2}\sqrt{14^2+(-4)^2+(-10)^2}=\frac{1}{2}\sqrt{196+16+100}=\frac{1}{2}\sq rt{312}$