Posted by Anonymous on .
let p=(1,1,1), Q=(2,3 5), and R=(1,3,1). find the area A of thr triangle with vertices P,Q, and R

calculas 
Steve,
get the sides of the triangle, then use Heron's formula:
PQ = √(1^2+2^2+4^2) = √21
QR = √(3^2+0^2+4^2) = 5
RP = √(2^2+2^2+0^2) = √8
I'll let you use Heron's formula. Probably better to convert to decimals rather than having all those nested roots. 
OR  calculus 
Reiny,
area of triange = (1/2)vector PQ x vector PR
vector PQ = [1,2,4] and vector PR = [2, 2,0}
PQ X PR = [8,8,6]
area = (1/2)√(64+64+36) = 1/2 √164
= 1/2 (2√41) = √41 
calculus  duh 
Steve,
good job, Reiny. Forgot about vectors!