Question:
\(\ \vec{k}\cdot(\vec{i}+\vec{j})=\) ?
\(\ \vec{k}\cdot(\vec{i}+\vec{j})=\) ?
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Orthogonal basis: $\,\vec{i}\perp\vec{j}\perp\vec{k}\,$ with unit lengths.
Updated On: Oct 17, 2025
- \(0\)
- \(1\)
- \(2\)
- \(-1\)
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The Correct Option is A
Solution and Explanation
\(\vec{k}\) is perpendicular to both \(\vec{i}\) and \(\vec{j}\). Dot product of perpendicular vectors is \(0\). Hence \(\vec{k}\cdot\vec{i}=0=\vec{k}\cdot\vec{j}\Rightarrow \vec{k}\cdot(\vec{i}+\vec{j})=0\).
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