alleryThe projection of $\mathbf{A}$ onto $\mathbf{B}$ is proportional to
A$\mathbf{A}\times\mathbf{B}$
B$\dfrac{\mathbf{A}\cdot\mathbf{B}}{\|\mathbf{B}\|}\cdot\dfrac{\mathbf{B}}{\|\mathbf{B}\|}$
C$\dfrac{\mathbf{A}\times\mathbf{B}}{\|\mathbf{A}\|}$
D$\dfrac{\mathbf{B}\cdot\mathbf{B}}{\|\mathbf{A}\|}\cdot\mathbf{A}$
Answer & Solution
Correct answer: B. $\dfrac{\mathbf{A}\cdot\mathbf{B}}{\|\mathbf{B}\|}\cdot\dfrac{\mathbf{B}}{\|\mathbf{B}\|}$
From the given formula, $\operatorname{proj}_{\mathbf{B}}\mathbf{A}=\dfrac{\mathbf{A}\cdot\mathbf{B}}{\|\mathbf{B}\|}\cdot\dfrac{\mathbf{B}}{\|\mathbf{B}\|}$.
This gives a vector along $\mathbf{B}$ whose magnitude equals the scalar projection of $\mathbf{A}$ on $\mathbf{B}$.
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