Chapter 8 - Polar Coordinates; Vectors - Section 8.7 The Cross Product - 8.7 Assess Your Understanding - Page 652: 47

$\sqrt {555}$

1. Find the vectors $\vec {P_1P_2}=<-3,1,4>$ and $\vec {P_1P_3}=$<-1,-4,3> 2. Find the cross product $\vec {P_1P_2}\times\vec {P_1P_3} = <(1(3)-4(-4)),(4(-1)-(-3)(3)),(-3(-4)-1(-1))>=<19,5,13>$ 3. We have the area $A=||\vec {P_1P_2}\times\vec {P_1P_3} || =\sqrt {19^2+5^2+13^2}=\sqrt {555}$