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. $$ | \mathbf{v} \|=25, \quad \alpha=330^{\circ} $$
Added by Barbara C.
Step 1
We can use trigonometry to do this. The angle $\alpha$ is given as $330^\circ$, which is in the fourth quadrant. We can find the angle $\theta$ between the vector $\mathbf{v}$ and the positive $x$-axis by subtracting $360^\circ$ from $\alpha$ to get $30^\circ$. Show moreβ¦
Show all steps
Close
Your feedback will help us improve your experience
Gregory Higby and 63 other Calculus 2 / BC educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Write the vector $\mathbf{v}$ in the form $a \mathbf{i}+b \mathbf{j},$ given its magnitude $\|\mathbf{v}\|$ and the angle $\alpha$ it makes with the positive $x$ -axis. $$\| \mathbf{v} \|=25, \quad \alpha=330^{\circ}$$
Polar Coordinates; Vectors
Vectors
Write the vector $\mathbf{v}$ in the form $\mathbf{a} \mathbf{i}+b \mathbf{j},$ given its magnitude $\|\mathbf{v}\|$ and the angle $\alpha$ it makes with the positive $x$ -axis. $$ \|\mathbf{v}\|=25, \quad \alpha=330^{\circ} $$
Write the vector $\mathbf{v}$ in the form $\mathbf{ai}+ \mathbf{bj}$, given its magnitude $\|\mathbf{v}\|$ and the angle $\alpha$ it makes with the positive $x$ -axis. $\|\mathbf{v}\|=25, \quad \alpha=330^{\circ}$
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Watch the video solution with this free unlock.
EMAIL
PASSWORD