Vector Cross Product Magnitude (Jee Mains)

Scalar and Vector Products

Medium

Vector Cross Product Magnitude

Let $\vec a = 2\hat i - \hat j + \hat k$ and $\vec b = \lambda \hat j + 2\hat k,\,\,\lambda \in Z$ be two vectors, Let $\vec c = \vec a \times \vec b$ and $\vec d$ be a vector of magnitude 2 in yz-plane. If $\left| {\vec c} \right| = \sqrt {53}$ , then the maximum possible value of ${\left( {\vec c \cdot \vec d} \right)^2}$ is equal to :

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