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 2u2 \mathbf{u}. This means we need to scale the vector u\mathbf{u} by a factor of 2.

Step 2: Scale the Vector

If u=[u1u2]\mathbf{u} = \begin{bmatrix} u_1 \\ u_2 \end{bmatrix}, then 2u=[2u12u2]2 \mathbf{u} = \begin{bmatrix} 2u_1 \\ 2u_2 \end{bmatrix}.

Final Answer

The vector 2u2 \mathbf{u} is obtained by scaling each component of u\mathbf{u} by 2.

{"axisType": 3, "coordSystem": {"xmin": -10, "xmax": 10, "ymin": -10, "ymax": 10}, "commands": ["y = 2u"], "latex_expressions": ["2mathbfu2 \\mathbf{u}"]}

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