alleryFor nonzero vector $\mathbf{A}$, which expression gives a vector in the same direction as $\mathbf{A}$ but of magnitude $1$?
A$\|\mathbf{A}\|\,\mathbf{A}$
B$\dfrac{\mathbf{A}}{\mathbf{A}\cdot\mathbf{A}}$
C$\dfrac{\mathbf{A}}{\|\mathbf{A}\|}$
D$\mathbf{A}\cdot\mathbf{A}$
Answer & Solution
Correct answer: C. $\dfrac{\mathbf{A}}{\|\mathbf{A}\|}$
Dividing a nonzero vector by its magnitude normalizes it, producing the unit vector $\hat{\mathbf{A}}=\mathbf{A}/\|\mathbf{A}\|$.
**Option B does not generally give magnitude $1$.**
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