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To determine the direction in which vector **v** points, we can calculate its angle with respect to the positive x-axis. The vector **v** is given by \( \vec{v} = \langle -10, 10 \rangle \), where the x-component is -10 and the y-component is 10.

### Step 1: Calculate the angle (θ)
The direction of the vector can be found using the formula for the angle θ between the vector and the positive x-axis:

\[
\theta = \tan^{-1}\left(\frac{y}{x}\right)
\]

For \( \vec{v} = \langle -10, 10 \rangle \):

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

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

### Step 2: Adjust for the quadrant
Since the vector has a negative x-component and a positive y-component, it lies in the second quadrant. To find the actual angle from the positive x-axis, we add 180° to the calculated angle:

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

### Conclusion:
The vector \( \vec{v} = \langle -10, 10 \rangle \) points at an angle of **135°** counterclockwise from the positive x-axis.

Would you like further details or have any questions?

Here are 5 related questions:
1. What is the magnitude of vector \( \vec{v} \)?
2. How would the direction change if the x-component were positive?
3. Can you find the unit vector in the direction of \( \vec{v} \)?
4. How can you express the vector \( \vec{v} \) in polar coordinates?
5. What would be the result if you added another vector to \( \vec{v} \)?

**Tip**: The quadrant a vector lies in is determined by the signs of its x- and y-components.

What direction does vector v point? v = <-10, 10>

Learn how to find the direction of vector v = <-10, 10> by calculating the angle using the inverse tangent function. The vector lies in the second quadrant and points at 135° from the positive x-axis. Suitable for high school students in Grades 9-12.

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