components  Ax2=
  -5.90  m
  ,  Ay2=
  -3.10  m
  Find the direction of the vector  A2→
 . Let the direction of a vector be the angle that the vector makes with the +x-axis, measured counterclockwise from that axis.

To find the direction of the vector \( \mathbf{A_2} \) from its components \( A_{x2} = -5.90 \, \text{m} \) and \( A_{y2} = -3.10 \, \text{m} \), we use the arctangent function to compute the angle.

The formula for the direction of the vector \( \mathbf{A_2} \) is:

\[
\theta = \tan^{-1}\left(\frac{A_{y2}}{A_{x2}}\right)
\]

Substitute the values of \( A_{x2} \) and \( A_{y2} \):

\[
\theta = \tan^{-1}\left(\frac{-3.10}{-5.90}\right)
\]

Let's calculate that angle and adjust it to the correct quadrant since both components are negative, indicating that the vector lies in the third quadrant. For vectors in the third quadrant, we add 180° to the calculated angle to express it as a positive angle measured counterclockwise from the +x-axis.

Let me calculate that for you.The direction of the vector \( \mathbf{A_2} \) is approximately \( 207.72^\circ \), measured counterclockwise from the positive \( x \)-axis. This angle places the vector in the third quadrant, which aligns with the signs of the given components.

Would you like more details or have any questions? Here are 5 related questions for practice:

1. What is the magnitude of vector \( \mathbf{A_2} \)?
2. How would the direction change if \( A_{x2} \) were positive while \( A_{y2} \) remains negative?
3. What is the direction if both components \( A_{x2} \) and \( A_{y2} \) were positive?
4. How do you compute the direction for a vector in the fourth quadrant?
5. How would the direction be affected if the magnitude of both components doubled?

**Tip:** Always double-check which quadrant the vector lies in when calculating the angle, as this affects whether you need to adjust the angle.

components Ax2 = -5.90 m, Ay2 = -3.10 m. Find the direction of the vector A2→. Let the direction of a vector be the angle that the vector makes with the +x-axis, measured counterclockwise from that axis.

Learn how to find the direction of a vector with components Ax = -5.90 m and Ay = -3.10 m using trigonometry. This problem involves calculating the angle the vector makes with the +x-axis, measured counterclockwise, and adjusting for the third quadrant. Ideal for students in Grades 10-12.

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