Finding equations

Question

 

Answer 1

Plane equation

x = (x0,y0,z0)+s(a,b,c)+t(d,e,f)

 =(-9,-6,3)+s((-6+3)/√((-3)^2+(-6)^2+(-6)^2),(-9+3)/√((-3)^2+(-6)^2+(-6)^2),

   (-9+3)/√((-3)^)2+(-6)^2+(-6)^2))+t((-6+3)/√((-3)^2+(-6)^2+(-6)^2),(-9+3)/√((-3)^2+(-6)^2+(-6)^2),    (-9+3)/√((-6)^2+(-3)^2+(6)^2))

=(-9,-6,3)+s(-3/√81,(-6)/√81,(-6)/√81)+t(-6/√81,(-3)/√81,6/√81)

=(-9,-6,3)+s(-3/9,(-6)/9,(-6)/9)+t(-6/9,(-3)/9,6/9)

   =(-9,-6,3)+s(-1/3,-2/3,-2/3)+t(-2/3,-1/3,2/3)

 

x = (x0,y0,z0)+s(a,b,c)+t(d,e,f)

 =(-3,-3,-3)+s((-9+3)/√((-6)^2+(-3)^2+(6)^2),(-6+3)/√((-6)^2+(-3)^2+(6)^2,

   (3+3)/√((-6)^2+(-3)^2+(6)^2)+t((-6+3)/√((-3)^2+(-6)^2+(-6)^2),(-9+3)/√((-3)^2+(-6)^2+(-6)^2),    (-9+3)/√((-3)^2+(-6)^2+(-6)^2))

=(-3,-3,-3)+s(-6/√81,(-3)/√81,(6)/√81)+t(-3/√81,(-6)/√81,-6/√81)

=(-3,-3,-3)+s(-6/9,(-3)/9,(6)/9)+t(-3/9,(-6)/9,-6/9)

   =(-3,-3,-3)+s(-2/3,-1/3,2/3)+t(-1/3,-2/3,-2/3)

So option 3,4 are correct

Comments

Explained other part also