$$\vec{a} \times \vec{b} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\\\ 2 & 3 & 1 \\\\ 1 & -1 & 2 \end{vmatrix}$$
$= \hat{i}(6+1) - \hat{j}(4-1) + \hat{k}(-2-3) = 7\hat{i} - 3\hat{j} - 5\hat{k}$
Back to JEE Main 2020 Vectors & 3D Geometry
JEE Main 2020 — Mathematics Vectors & 3D Geometry
medium
mcq
2020
Official previous-year question
Verified 30 May 2026.
Question
If $\vec{a} = 2\hat{i} + 3\hat{j} + \hat{k}$ and $\vec{b} = \hat{i} - \hat{j} + 2\hat{k}$, then $\vec{a} \times \vec{b}$ is:
Options
- A
$7\hat{i} - 3\hat{j} - 5\hat{k}$
- B
$7\hat{i} + 3\hat{j} - 5\hat{k}$
- C
$-7\hat{i} + 3\hat{j} + 5\hat{k}$
- D
$7\hat{i} - 3\hat{j} + 5\hat{k}$
Solution
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