Question

Find the direction and magnitude of vector aƒ— bƒ—.

Answer 1

To find the direction and magnitude of vector aƒ— bƒ—, resolve the vectors into their components, add the x and y components separately, and then find the magnitude and direction of the resultant vector.

Step-by-step explanation:

To find the direction and magnitude of vector aƒ— bƒ—, we need to perform vector addition. Assuming we have the magnitudes and direction angles of vectors a and b, we can use the following steps:

1. Resolve vector a into its x and y components using the magnitude and direction angle.
2. Resolve vector b into its x and y components using the magnitude and direction angle.
3. Add the x components and y components separately.
4. Find the magnitude of the resultant vector by taking the square root of the sum of the squares of the x and y components.
5. Find the direction of the resultant vector using the arctan function to calculate the angle between the resultant vector and the positive x-axis.

For example, if vector a has a magnitude of 5 and a direction angle of 30 degrees, and vector b has a magnitude of 3 and a direction angle of 60 degrees, we can find the resultant vector as follows:

1. ax = 5 * cos(30) = 4.33
2. ay = 5 * sin(30) = 2.5
3. bx = 3 * cos(60) = 1.5
4. by = 3 * sin(60) = 2.6
5. rx = ax + bx = 4.33 + 1.5 = 5.83
6. ry = ay + by = 2.5 + 2.6 = 5.1
7. Magnitude of resultant vector = sqrt(rx^2 + ry^2) = sqrt(5.83^2 + 5.1^2) = 7.63
8. Direction of resultant vector = arctan(ry/rx) = arctan(5.1/5.83) = 44.93 degrees