How can one find the magnitude and the directions of a resultant if Vector A is 35N @ 60' NE, and Vector B is 50N @ 20' NW?

See your previous post for solution.

To find the magnitude and direction of the resultant vector, we can use vector addition. Here are the steps:

1. Draw Vector A and Vector B on a coordinate system.
- Place Vector A starting from the origin (0,0) and extend it 35 units at an angle of 60° northeast (45° clockwise from the positive x-axis).
- Place Vector B starting from the same origin (0,0) and extend it 50 units at an angle of 20° northwest (45° counterclockwise from the positive x-axis).

2. Use the components method to break down Vector A and Vector B into their x and y components.
- For Vector A:
- x-component = magnitude * cos(angle) = 35N * cos(60°)
- y-component = magnitude * sin(angle) = 35N * sin(60°)
- For Vector B:
- x-component = magnitude * cos(angle) = 50N * cos(20°)
- y-component = magnitude * sin(angle) = 50N * sin(20°)

3. Add the x-components and y-components of Vector A and Vector B separately.
- x-component of the resultant = sum of x-components of Vector A and Vector B
- y-component of the resultant = sum of y-components of Vector A and Vector B

4. Use the Pythagorean theorem to find the magnitude of the resultant vector.
- magnitude of the resultant = sqrt((x-component of the resultant)^2 + (y-component of the resultant)^2)

5. Use trigonometry to find the direction (angle) of the resultant vector.
- direction of the resultant = arctan((y-component of the resultant) / (x-component of the resultant))

By following these steps, you should be able to find the magnitude and direction of the resultant vector.

To find the magnitude and direction of the resultant of Vector A and Vector B, you can follow these steps:

Step 1: Convert the given vectors into their horizontal and vertical components. To do this, you can use trigonometry.

For Vector A, the magnitude is 35N, and the direction is 60 degrees northeast. To find the horizontal component (Ax) and vertical component (Ay), you can use the following equations:

Ax = A * cos(theta)
Ay = A * sin(theta)

where A is the magnitude and theta is the angle.

Ax = 35N * cos(60 degrees)
Ay = 35N * sin(60 degrees)

Similarly, for Vector B, the magnitude is 50N, and the direction is 20 degrees northwest:

Bx = B * cos(theta)
By = B * sin(theta)

Bx = 50N * cos(20 degrees)
By = 50N * sin(20 degrees)

Step 2: Add the horizontal components and vertical components to find the resultant components:

Rx = Ax + Bx
Ry = Ay + By

Step 3: Find the magnitude of the resultant using the Pythagorean theorem:

Magnitude of resultant (R) = sqrt(Rx^2 + Ry^2)

Step 4: Find the direction of the resultant using trigonometry:

Direction of resultant = atan(Ry / Rx)

Thus, by following these steps, you can find the magnitude and direction of the resultant.