The value of k, so that the points (1, 2, 3,) (k, 0, 4) and (-2, 4, 2) will be in a line -

Explanation

The given point will be collinear if $$ \begin{vmatrix} 1 & 2 & 2 & 3 \\ k & 0 & 0 & 4 \\ -2 & 4 & 4 & 2 \end{vmatrix} = 0 $$ $$\Rightarrow 1 \begin{vmatrix} 0 & 4 \\ 4 4 & 2 \end{vmatrix} - 2 \begin{vmatrix} k & 4 \\ -2 & 2 \end{vmatrix} + 3 \begin{vmatrix} k & 0 \\ -2 & 4 \end{vmatrix} = 0$$ $$\Rightarrow 1(0 - 16) - 2(2k + 8) + 3(4k) = 0$$ $$\Rightarrow -16 - 4k - 16 + 12k = 0$$ $$\Rightarrow 8k = 32$$ $$\Rightarrow k = 4$$ ## Page 27