Chapter 8 - Polar Coordinates; Vectors - Section 8.7 The Cross Product - 8.7 Assess Your Understanding - Page 652: 48

$\sqrt {217}$

1. Find the vectors $\vec {P_1P_2}=< 4, 1,-3>$ and $\vec {P_1P_3}=< 4, -1, 0>$ 2. Find the cross product $\vec {P_1P_2}\times\vec {P_1P_3} = <(1(0)-(-3)(-1)),(-3(4)-4(0)),(4(-1)-1(4))>=<-3,-12,-8>$ 3. We have the area $A=||\vec {P_1P_2}\times\vec {P_1P_3} || =\sqrt {3^2+12^2+8^2}=\sqrt {217}$