B x equals negative 96.0 meters and  B y equals negative 78.9 meters. Find the direction of the vector. Blank degrees; fill in the blank.

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.

B x equals negative 96.0 meters and B y equals negative 78.9 meters. Find the direction of the vector.

Learn how to find the direction of a vector with components Bx = -96.0 meters and By = -78.9 meters using the arctangent function. This solution includes the calculation of the angle with respect to the x-axis and explains how to interpret the result based on the quadrant. Suitable for Grades 10-12 students learning trigonometry and vectors.

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