Question
a. Consider a vector $\vec{v}$ in $\mathbb{R}^{n},$ and a scalar $k .$ Show that$$\|k \vec{v}\|=|k|\|\vec{v}\|$$b. Show that if $\vec{v}$ is a nonzero vector in $\mathbb{R}^{n},$ then $\vec{u}=\frac{1}{\|\vec{v}\|} \vec{v}$ is a unit vector.
Step 1
For a vector \(\vec{v} = (v_1, v_2, \ldots, v_n)\) in \(\mathbb{R}^n\), the norm \(\|\vec{v}\|\) is defined as: \[ \|\vec{v}\| = \sqrt{v_1^2 + v_2^2 + \cdots + v_n^2} \] Show more…
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