Vector Dot Product Calculation (Jee Mains)

Scalar and Vector Products

Medium

Vector Dot Product Calculation

Let $\vec a = 2\hat i + \hat j - 2\hat k$ , $\vec b = \hat i + \hat j$ and $\vec c = \vec a \times \vec b$ . Let $\vec d$ be a vector such that $\left| {\vec d - \vec a} \right| = \sqrt {11} ,\left| {\vec c \times \vec d} \right| = 3$ and the angle between $\vec c$ and $\vec d$ is $\frac{\pi }{4}$ . Then $\vec a \cdot \vec d$ is equal to

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