Write the vector in the form Ka,b) 140° The vector is ). (Simplify your answer. Do not round until the final answer. Then round to four decimal places as needed.) 3.
Write the vector in the form Ka,b) 140° The vector is ). (Simplify your answer. Do not round until the final answer. Then round to four decimal places as needed.) 3.
Write the vector in the form Ka,b) 140° The vector is ). (Simplify your answer. Do not round until the final answer. Then round to four decimal places as needed.) 3.
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### Write the vector in the form \(\langle a,b\rangle \)
This image contains a diagram of a vector \(\mathbf{v}\) in the standard Cartesian coordinate system.
**Diagram Explanation:**
- A 2D Cartesian coordinate system is depicted with the x-axis horizontal and the y-axis vertical.
- The vector \(\mathbf{v}\) is shown originating from the origin (0,0) and pointing in the direction of 140° counterclockwise from the positive x-axis.
- The magnitude of the vector \(\mathbf{v}\) is 3 units.
#### Task:
Convert the given vector \(\mathbf{v}\) to its component form \(\langle a, b \rangle\).
#### Instructions:
1. To find the components of the vector \(\mathbf{v}\), use the formulas:
\[
a = 3 \cos(140^\circ)
\]
\[
b = 3 \sin(140^\circ)
\]
2. Calculate the values of \(a\) and \(b\).
3. Simplify your answers without rounding until the final step.
4. Round the final answers to four decimal places if needed.
```
The vector is \(\langle \text{____} , \text{____} \rangle\).
```
(Simplify your answer. Do not round until the final answer. Then round to four decimal places as needed.)
---
Feel free to fill in the image link and the calculated values for a complete educational resource.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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This image contains a diagram of a vector \(\mathbf{v}\) in the standard Cartesian coordinate system.
**Diagram Explanation:**
- A 2D Cartesian coordinate system is depicted with the x-axis horizontal and the y-axis vertical.
- The vector \(\mathbf{v}\) is shown originating from the origin (0,0) and pointing in the direction of 140° counterclockwise from the positive x-axis.
- The magnitude of the vector \(\mathbf{v}\) is 3 units.
#### Task:
Convert the given vector \(\mathbf{v}\) to its component form \(\langle a, b \rangle\).
#### Instructions:
1. To find the components of the vector \(\mathbf{v}\), use the formulas:
\[
a = 3 \cos(140^\circ)
\]
\[
b = 3 \sin(140^\circ)
\]
2. Calculate the values of \(a\) and \(b\).
3. Simplify your answers without rounding until the final step.
4. Round the final answers to four decimal places if needed.
```
The vector is \(\langle \text{____} , \text{____} \rangle\).
```
(Simplify your answer. Do not round until the final answer. Then round to four decimal places as needed.)
---
Feel free to fill in the image link and the calculated values for a complete educational resource.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fac5ee0c2-989a-419f-9731-ea881b743b03%2F8bd32d0a-21aa-48de-a714-30fe30afdc9c%2Feg8clgs_processed.png&w=3840&q=75)
