1. The problem statement, all variables and given/known data The vectors a= <-4,3,3> and b = <2,-6,-5> are parallel to a plane PI and R is a point on with position vector <104,8,-6> . Find the Cartesian equation of the plane. What is the distance of the plane from the origin? 2. Relevant equations 3. The attempt at a solution This is my thinking. Since we are told the vectors a and b are parallel to the plane if we cross them we can get a vector perpendicular to the plane. We can turn that into a unit vector and dot it with the point r. So, a cross b = <3,-14,18> : call this vector v v = √(3^2) + (-14^2)+(18)^2 = 23 So v(hat) = 1/23<3,-14,18> Then to get the equation of the plane we can do x dot v(hat) = r dot v(hat) <x,y,z> dot 1/23<3,-14,18> = <104,8,-6> dot <1/23<3,-14,18> So I got 3/23x - 14/23y + 18/23z = 92/23 Then just multiply through to clear out the fraction 3x - 14y +18z = 92 and the distance from the plane to the origin is 4 units because r dot v hat is 4 Did I do this correct?