Question

Consider the three displacement vectors ( mathbfa = 5hati + 13hatj ) m, ( mathbfb = 5hati + 4hatj ) m, and ( mathbfc = 12hati + 5hatj ) m. Use the component method to determine:

(a) The magnitude and direction of ( mathbfd = mathbfa + mathbfb + mathbfc ).

(b) The magnitude and direction of ( mathbfe = 2mathbfa + mathbfb + mathbfc ).

Answer 1

To find the magnitude and direction of the displacement vector D, add the x and y components of the given displacement vectors A, B, and C.

Step-by-step explanation:

To find the magnitude and direction of the displacement vector D = A + B + C, we need to add the x and y components of the three given displacement vectors. when the current in the wire decreases, the magnetic field around the coil also decreases. In response, the induced current will flow in the same direction as the original current to try to maintain the magnetic field.

The x component of D is the sum of the x components of A, B, and C: x_D = x_A + x_B + x_C. The y component of D is the sum of the y components of A, B, and C: y_D = y_A + y_B + y_C.

Once we have the x and y components, we can calculate the magnitude of D using the Pythagorean theorem: |D| = sqrt(x_D^2 + y_D^2). To find the direction of D, we can use inverse tangent: theta_D = arctan(y_D / x_D).