Find all values of $$\lambda $$ such that $$x, y, z,$$$$\, \ne $$$$(0,0,0)$$ and
$$\left( {\overrightarrow i + \overrightarrow j + 3\overrightarrow k } \right)x + \left( {3\overrightarrow i - 3\overrightarrow j + \overrightarrow k } \right)y + \left( { - 4\overrightarrow i + 5\overrightarrow j } \right)z$$
$$ = \lambda \left( {x\overrightarrow i \times \overrightarrow j \,\,y + \overrightarrow k \,z} \right)$$ where $$\overrightarrow i ,\,\,\overrightarrow j ,\,\,\overrightarrow k $$ are unit vectors along the coordinate axes.