Chapter 8 - Polar Coordinates; Vectors - Section 8.7 The Cross Product - 8.7 Assess Your Understanding - Page 652: 46

$\sqrt {213}$

1. Find the vectors $\vec {P_1P_2}=< 2, 3, 1>$ $\vec {P_1P_3}=<-2,4,1>$ 2. Find the cross product $\vec {P_1P_2}\times\vec {P_1P_3} = <(3(1)-1(4)),(1(-2)-2(1)),(2(4)-3(-2))>=<-1,-4,14>$ 3. We have the area $A=||\vec {P_1P_2}\times\vec {P_1P_3} || =\sqrt {1^2+4^2+14^2}=\sqrt {213}$