Vector Algebra
Oswaal
CBSE
Grade 12
Question:
If $\vec{a} = \hat{i} + \hat{j} + \hat{k}, \vec{b} = \hat{i} + 2\hat{j} + 3\hat{k}$ and $\vec{c} = \hat{i} - \hat{j} + \hat{k}$, find a unit vector $\hat{d}$ such that $\vec{d} \cdot \vec{a} = 0, \vec{d} \cdot \vec{b} = 0$ and $\vec{d} \cdot \vec{c} > 0$.
Step-by-Step Solution
Key Concept: \hat{d} = (\hat{i} - 2\hat{j} + \hat{k})/\sqrt{6}.
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Correct Answer:
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