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Solve the following.
If is a unit vector perpendicular to and , find .
If $\vec{a}$ is a unit vector perpendicular to $\vec{b}$ and $(\vec{a} + 2\vec{b}) \cdot (3\vec{a} - \vec{b}) = -5$, find $|\vec{b}|$.
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From ISC 2025 Specimen Mathematics Paper 1, question 15(iv).
Check your working with the 3D geometry and vectors calculator: points, vectors, lines and planes: distances, angles, foot and image, shortest distance, intersections.