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Vectors Practice Test
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Q1
A drone flies in a steady wind, modeled with vectors (magnitude and direction). The drone’s air-velocity is $\vec{d}=6\mathbf{i}+1\mathbf{j}+0\mathbf{k}$ (m/s), and the wind velocity is $\vec{w}=-2\mathbf{i}+3\mathbf{j}+0\mathbf{k}$ (m/s). The drone’s ground velocity is the vector sum $\vec{g}=\vec{d}+\vec{w}$ because both effects act simultaneously. Subtraction represents “removing” an effect: if you know $\vec{g}$ and $\vec{w}$, then $\vec{d}=\vec{g}-\vec{w}$. The coordinate axes use $x$ east and $y$ north; arrows indicate direction. Refer to the vectors described in the passage. Determine the magnitude of the resultant vector $\vec{g}$.
A drone flies in a steady wind, modeled with vectors (magnitude and direction). The drone’s air-velocity is $\vec{d}=6\mathbf{i}+1\mathbf{j}+0\mathbf{k}$ (m/s), and the wind velocity is $\vec{w}=-2\mathbf{i}+3\mathbf{j}+0\mathbf{k}$ (m/s). The drone’s ground velocity is the vector sum $\vec{g}=\vec{d}+\vec{w}$ because both effects act simultaneously. Subtraction represents “removing” an effect: if you know $\vec{g}$ and $\vec{w}$, then $\vec{d}=\vec{g}-\vec{w}$. The coordinate axes use $x$ east and $y$ north; arrows indicate direction. Refer to the vectors described in the passage. Determine the magnitude of the resultant vector $\vec{g}$.