Equation of plane question?

Question about vectors?

• Hi, I'm studying for my final exam for vectors but I dont understand some of the questions my teacher left for review and i need to know the procedure on how to do this questions in order to pass so here it is: Question 1: find the value of "a" such that the plane with equation 2x + 3y + az - 8 = 0 is parallel to the line with equation (x - 1)/2 = (y - 2)/3 = z + 1 please help i would really appreciated

• Answer:

  From the cartesian equation of a plane 2x + 3y + az = 8 we can see that a normal vector to the plane is: <2,3,a> Putting the symmetric equations of the line (x - 1)/2 = (y - 2)/3 = z + 1 to vector form we get: <1 +2t, 2 +3t, -1 +t> and from this vector form we can see that a vector parallel to the line would be: <2, 3, 1> Now, in order for the plane to be parallel to the line, the dot product of the normal vector of the plane <2,3,a> and the vector parallel to the line <2, 3, 1> must be orthogonal ( equal 0). In other words, <2,3,a> dot <2, 3, 1> = 0 2(2) + 3(3) + 1(a) = 0 a = -13