(Solved): Part A - Geometric addition What are the magnitude and direction of the resultant vector, R , when ...

Part A - Geometric addition What are the magnitude and direction of the resultant vector, R , when the parallelogram law is applied to A and B ? Express the magnitude to three significant figures. Express the angle to one decimal place, measured counterclockwise from the positive x axis. Separate your answers by a comma.

Part B - Component addition of vectors

What is the resultant vector, R, obtained by adding vectors C and D?

Express the magnitude to three significant figures. Express the angle to one decimal place, measured counterclockwise from the positive x axis. Separate your answers by a comma.

Part C - Addition of more than two vectors

Now we wish to add all four vectors. Attempting to do this using the parallelogram method is difficult because that method is optimized for two vectors. It is much easier to use vector components when there are more than two vectors being added.For the vector sum R=A+B+C+D, what are the magnitude and direction of the resultant R?

Express the magnitude to three significant figures. Express the angle to one decimal place, measured counterclockwise from the positive x axis. Separate your answers by a comma.

Learning Goal: To use geometric and component addition of vectors. Four vectors \( \mathbf{A}, \mathbf{B}, \mathbf{C} \), and \( \mathbf{D} \) are shown (not to scale). Vector \( \mathbf{A} \) has magnitude \( 21.7 \) and acts at an angle of \( 13.7 \) degrees with respect to the positive \( x \) axis. Vector \( \mathbf{B} \) has magnitude \( 12.7 \) and acts at an angle of \( 70.7 \) degrees with respect to the positive \( x \) axis. Vector \( \mathbf{C} \) has magnitude \( 29.1 \) and acts at an angle of \( 147.3 \) degrees with respect to the positive \( x \) axis. Vector \( \mathbf{D} \) has magnitude \( 10.0 \) and acts at an angle of 285.1 degrees with respect to the positive \( x \) axis.(Figure 1)