Question

If the planes x-ky-z=0, kx-y-z=0, x+y-z=0 meet in a line, then the sum of possible values of k are

Answer 1

here is ur ans⤵

For the given homogeneous system to have non zero solution determinant of coefficient matrix should be zero.

(i.e) $\begin{vmatrix}1 &-k &-1\\k&-1&-1\\1 &1&-1\end{vmatrix}$

$\Rightarrow 1(1+1)+k(-k+1)-1(k+1)=0$

$\Rightarrow 2-k^2+k-k-1=0$

$k^2=1$

$k=\pm 1$

hope it helps