Questions: Sketch the vector indicated. (The vectors u and v are shown in the following figure.) 2u

Sketch the vector indicated. (The vectors u and v are shown in the following figure.) 2u
Transcript text: Sketch the vector indicated. (The vectors $\mathbf{u}$ and $\mathbf{v}$ are shown in the following figure.) \[ 2 \mathbf{u} \]
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Solution

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Solution Steps

Step 1: Identify the Vector

The vector given is \(2 \mathbf{u}\). This means we need to scale the vector \(\mathbf{u}\) by a factor of 2.

Step 2: Scale the Vector

If \(\mathbf{u} = \begin{bmatrix} u_1 \\ u_2 \end{bmatrix}\), then \(2 \mathbf{u} = \begin{bmatrix} 2u_1 \\ 2u_2 \end{bmatrix}\).

Final Answer

The vector \(2 \mathbf{u}\) is obtained by scaling each component of \(\mathbf{u}\) by 2.

{"axisType": 3, "coordSystem": {"xmin": -10, "xmax": 10, "ymin": -10, "ymax": 10}, "commands": ["y = 2u"], "latex_expressions": ["$2 \\mathbf{u}$"]}

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