Find the vector $v$ with the given length and the same direction as $\mathbf{u}$. $$\|\mathbf{v}\|=5, \quad \mathbf{u}=(\sqrt{5}, 5,0)$$
Added by Javier E.
Step 1
We can do this by dividing $\mathbf{u}$ by its magnitude: $$\mathbf{\hat{u}} = \frac{\mathbf{u}}{\|\mathbf{u}\|} = \frac{1}{\sqrt{5^2+5^2}}(\sqrt{5},5,0) = \left(\frac{1}{\sqrt{10}},\frac{1}{\sqrt{10}},0\right)$$ Show more…
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