If the component of the vector $\vec{A}$ along the vector $\vec{B}$ is twice the component of $\vec{B}$ along $\vec{A}$, then the ratio of magnitudes of vectors $\vec{A}$ and $\vec{B}$ is
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The projection of $\vec{P}$ on $\vec{Q}$ is $\vec{P} \cdot \hat{Q}$. This depends inversely on the magnitude of the vector being projected *on*.