Scalar and vector product of two vectorsMedium

Maximum Magnitude of Cross Product Vector

Let $\vec a = 2\hat i - \hat j + 3\hat k$ , $\overrightarrow b = 3\hat i - 5\hat j + \hat k$ and $\overrightarrow c$ be a vector such that $\overrightarrow a \times \overrightarrow c = \overrightarrow c \times \overrightarrow b$ and $\left( {\overrightarrow a + \overrightarrow c } \right).\left( {\overrightarrow b + \overrightarrow c } \right)$ = 168. Then the maximum value of ${\left| {\overrightarrow c } \right|^2}$ is :

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