Question
Write the vector $\mathbf{v}$ in the form $a \mathbf{i}+b \mathbf{j},$ given its magnitude $\|\mathbf{v}\|$ and the angle a it makes with the positive $x$ -axis.$$|\mathbf{v}|=5, \quad \alpha=60^{\circ}$$
Step 1
We can use these to find the components of the vector in the form $a\mathbf{i} + b\mathbf{j}$ using the formulas $a = |\mathbf{v}|\cos(\alpha)$ and $b = |\mathbf{v}|\sin(\alpha)$. Show more…
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