Find the area of the triangle if the vertices are:
A=(2,1)
B=(4,-1)
C=(6,3) using vector cross product.
$\displaystyle P_{1}(2,1), \;\ P_{2}(4,-1), \;\ P_{3}(6,3)$
$\displaystyle \overrightarrow{P_{1}P_{2}}=(2,-2)$
$\displaystyle \overrightarrow{P_{1}P_{3}}=(4,2)$
$\displaystyle \overrightarrow{P_{1}P_{2}}\times\overrightarrow{P _{1}P_{3}}=(0,0,12)$
$\displaystyle \frac{1}{2}||\overrightarrow{P_{1}P_{2}}\times\ove rrightarrow{P_{1}P_{3}}||=?$
Can you finish?.