Let
Then will be perpendicular to both and .
Could somebody please explain me how I should solve the following?
Determine the vector equation of the plane P(a) containing the line AB and perpendicular to the vector v(a).
Given
A(1,0,1) B(0,-1,1) and v(a) = i - j + (a)k
A plane perpendicular to vector <A, B, C> and containing point has equation
Here (1, 0, 1) is a point in the plane and <1, -1, a> is perpendicular to the plane so (x-1)- y+ a(z-1)= 0. We can write that as x- y+ az= a+1. We can solve for x: x= y- az+ a+ 1 and, using y and z as parameters write
.