Answer:
0.5*sqrt33
Explanation:
A(0,0,0) B(-4,1,-2), c(-4,2,-3)
Vector AB is (-4-0,-1-0, -2-0)= (-4,-1,-2) The modul of AB is sqrt (4squared+
+(-1) squared+ (-2) squared)= sqrt (16+1+4)=sqrt21
Vector AC is (-4,2,-3) The modul of vector AC is equal to sqrt ((-4)squared+ 2squared+(-3)squared)= sqrt(16+4+9)= sqrt29
Vector BC is equal to (-4-(-4), 2-1, -3-(-2))= (0,1,-1)
The modul of BC is sqrt (1^2+(-1)^2)=sqrt2
Find the angle B
Ac^2= BC^2+AB^2-2*BC*AB*cosB
29= 2+21-2*sqrt2*sqrt21*cosB
29= 2+21-2*sqrt42*cosB
cosB= -3/ sqrt42
sinB= sqrt( 1-(-3/sqrt42)^2)=sqrt33/42= sqrt11/14
s=1/2* (sqrt2*sqrt21*sqrt11/14)=1/2*sqrt(42*11/14)= 0.5*sqrt33