Let two rods placed on the ground be represented by vectors $4\hat{i} - \hat{j} + 3\hat{k}$ and $-2\hat{i} + \hat{j} - 2\hat{k}$. Find a vector representing a flag-post of height 5 m that has to be erected perpendicular to both the rods.
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Always double-check that your cross product is orthogonal to the original vectors by taking the dot product. Here, $(-\hat{i} + 2\hat{j} + 2\hat{k}) \cdot (4\hat{i} - \hat{j} + 3\hat{k}) = -4 - 2 + 6 = 0$. This guarantees absolute algebraic accuracy!