Vector Cross and Dot Product (Jee Mains)

Scalar and Vector Products

Medium

Vector Cross and Dot Product

Let $\overrightarrow a = 2\widehat i - 5\widehat j + 5\widehat k$ and $\overrightarrow b = \widehat i - \widehat j + 3\widehat k$ . If $\overrightarrow c$ is a vector such that $2\left( {\overrightarrow a \times \overrightarrow c } \right) + 3\left( {\overrightarrow b \times \overrightarrow c } \right) = \overrightarrow 0$ and $\left( {\overrightarrow a -\overrightarrow b } \right).\overrightarrow c$ = – 97 then ${\left| {\overrightarrow c \times \widehat k} \right|^2}$ is equal to

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