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Mathematics · 2026

JEE Main · 6 April 2026, Shift 1 · Q23

If a = i + j + k, b = j - k and c be three vectors such that a × c = b and a · c =3, then c ·( a -2 b ) is equal to ____.

If $\displaystyle \vec{a}=\hat{i}+\hat{j}+\hat{k}, \vec{b}=\hat{j}-\hat{k}$ and $\displaystyle \vec{c}$ be three vectors such that $\displaystyle \vec{a} \times \vec{c}=\vec{b}$ and $\displaystyle \vec{a} \cdot \vec{c}=3$, then $\displaystyle \vec{c} \cdot(\vec{a}-2 \vec{b})$ is equal to $\displaystyle \_\_\_\_$.
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JEE Main 2026 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.