- #1
Kernul
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- 7
Homework Statement
Find for what real parameters the line ##r## is parallel to the plane ##\pi##.
##r: \begin{cases}
x - 3y + 3 = 0 \\
2y + z - 5 = 0
\end{cases}##
##\pi : 6x - (a - 1)y + 3az - 11 = 0##
Homework Equations
The Attempt at a Solution
So, the only method I know is to put the three equations in a matrix, find the determinant, and see for what ##a## the determinant becomes ##0##.
##\begin{vmatrix}
6 & -(a - 1) & 3a & -11 \\
1 & -3 & 0 & 3 \\
0 & 2 & 1 & -5
\end{vmatrix}##
And I end up with ##a = \frac{5}{4}##.
But, since I'm not sure about my method, does anybody know how to proceed in these cases where the exercise involves real parameters?