To find the direction of the vector, we can calculate the angle it makes with the positive $x$-axis using the inverse tangent (arctangent) function. The formula is:

$\theta = \tan^{-1}\left(\frac{B_y}{B_x}\right)$

Given:

• $B_x = -96.0$ meters
• $B_y = -78.9$ meters

Substituting the values:

$\theta = \tan^{-1}\left(\frac{-78.9}{-96.0}\right)$

Now, let me calculate the angle.The direction of the vector is approximately $-140.6^\circ$. Since angles are typically measured counterclockwise from the positive $x$-axis, the negative value indicates that the vector is in the third quadrant. Alternatively, you can describe the direction as $219.4^\circ$ (by adding 360° to the negative angle).

Would you like more details on this or any related concepts?

Here are five related questions:

1. What is the formula for calculating the magnitude of a vector?
2. How do you convert between degrees and radians?
3. What does the direction of a vector signify in physics?
4. How can you determine which quadrant a vector is in?
5. What are the possible real-world interpretations of vector direction?

Tip: When working with vectors, always double-check the quadrant based on the signs of the vector's components.