Let and Let be a vector such that and the angle between and is . Then is equal to [2026]

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Solution

Q.
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 $| \vec{d} - \vec{a} |$ $= \sqrt{11},$ $| \vec{c} \times \vec{d} |$ $= 3$ and the angle between $\vec{c}$ and $\vec{d}$ is $\frac{π}{4}$ . Then $\vec{a} \cdot \vec{d}$ is equal to [2026]

1 3

2 1

3 0

4 11

Ans.
(3)

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