Find the direction angle of *v= (-10,10) Round* *your answer to the nearest tenth of a* *degree.*

To find the direction angle \(\theta\) of the vector \(\mathbf{v} = (-10, 10)\), we use the formula:

\[
\theta = \arctan\left(\frac{y}{x}\right)
\]

where \(x = -10\) and \(y = 10\).

\[
\theta = \arctan\left(\frac{10}{-10}\right) = \arctan(-1)
\]

The arctangent of \(-1\) is \(-45^\circ\). However, since \(x = -10\) and \(y = 10\), the vector lies in the second quadrant. In the second quadrant, the direction angle is:

\[
\theta = 180^\circ - 45^\circ = 135^\circ
\]

Rounded to the nearest tenth of a degree, the direction angle is:

\[
\theta = 135.0^\circ
\]

Would you like more details or have any questions?

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Here are 5 related questions:

1. What is the direction angle of the vector \(\mathbf{v} = (10, 10)\)?
2. How does changing the sign of the components affect the direction angle?
3. What is the magnitude of the vector \(\mathbf{v} = (-10, 10)\)?
4. How would you find the direction angle in radians instead of degrees?
5. How would you describe the relationship between the direction angle and the vector's components?

**Tip:** When determining the direction angle, always consider the quadrant where the vector lies. This helps to correctly adjust the angle from the arctan calculation.

Learn how to find the direction angle of the vector (-10, 10) using the arctangent formula and quadrant analysis. This problem covers vectors and trigonometry, suitable for Grades 10-12 students.

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