Find the value of \(x \) such that \(\mathbf{v} = \begin{pmatrix} 1 \\ 2 \\ x \end{pmatrix}\)is a vector parallel to the plane through the points \(A = (0,1,1), B = (1,1,0)\) and \(C = (1,0,3).\)
+128460 Here : https://web2.0calc.com/questions/please-help_34243
We found that the normal vector to the plane containing A, B , C was
(-1, - 3 , - 1)
The dot product of any vector parallel to the plane and the normal vector to the plane will = 0
So using ( 1, 2 , x) we have that
1(-1) + 2(-3) + x (-1) = 0
-1 - 6 - x = 0
-7 - x = 0
-7 = x
