Answer to Question #310468 in Analytic Geometry for Alex

Question

There is a triangle formed by the intersection of the following lines:

r1 = [0,1,7]+s[15,6,-12]

r2 = [4,-4,8]+s[4,-5,1]

r3 = [4,-4,8]+s[4,-5,1]

Find the area of this triangle

Answer 1

$r_1 = <0,1,7>+s_1<15,6,-12>\\ r_2 = <4,-4,8>+s_2<4,-5,1>\\ r_3 =<4,-4,8>+s_3<4,-5,1>\\ A=r_1\cap r_2\\ 0+15s_1=4+4s_2\\ 1+6s_1=-4-5s_2\\ 7-12s_1=8+s_2\\ s_2=-12s_1-1\\ 1+6s_1=-4+60s_1+5\\ s_1=0, s_2=-1\\ A(0,1,7)$

$r_2=r_3$

There is not a triangle formed by the intersection of the following lines