Find the angle that the vector R = A + B
makes with the positive x axis, use counter-
clockwise as the positive angular direction,
between the limits of −180 degrees and +180 degrees.
Answer in units of degrees
To find the angle between vector R and the positive x-axis, you can use the dot product formula and trigonometry. Here are the steps to find the angle:
1. Calculate the dot product of vectors A and B:
- If A = (A_x,A_y) and B = (B_x,B_y), then the dot product A ⋅ B = A_x * B_x + A_y * B_y.
2. Find the magnitudes of vectors A and B:
- The magnitude of a vector A = (A_x,A_y) can be calculated using the formula |A| = sqrt(A_x^2 + A_y^2).
3. Calculate the magnitude of vector R:
- Since R = A + B, calculate the magnitudes of A and B using the formulas above, then use the formula |R| = sqrt(A^2 + B^2 + 2 * A * B * cos(θ)), where θ is the angle between A and B.
4. Calculate the angle θ using the dot product:
- The dot product of A and B is given by A ⋅ B = |A| * |B| * cos(θ). Rearrange this equation to solve for cos(θ): cos(θ) = (A ⋅ B) / (|A| * |B|).
- Take the inverse cosine (cos^(-1)) of the expression above to find the angle θ in radians.
5. Convert the angle from radians to degrees:
- Multiply the angle in radians by (180 / π) to get the angle in degrees.
Note: Make sure to use counter-clockwise as the positive angular direction as specified.
By following these steps, you can find the angle that the vector R makes with the positive x-axis within the specified limits of -180 degrees to +180 degrees.