Question
If $\mathbf{v}=2 \mathbf{i}-\mathbf{j}$ and $\mathbf{w}=x \mathbf{i}+3 \mathbf{j}$, find all numbers $x$ for which $\|\mathbf{v}+\mathbf{w}\|=5$.
Step 1
Given \(\mathbf{v} = 2\mathbf{i} - \mathbf{j}\) and \(\mathbf{w} = x\mathbf{i} + 3\mathbf{j}\), we add the vectors component-wise: \[ \mathbf{v} + \mathbf{w} = (2\mathbf{i} - \mathbf{j}) + (x\mathbf{i} + 3\mathbf{j}) = (2 + x)\mathbf{i} + (-1 + 3)\mathbf{j} = (2 + Show more…
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