Question

You are given two vectors A = −3.00i +7.00j and B =6.00i +2.00j. Let counterclockwise angles be positive. What angle θA, where 0 ≤ θA < 360, does A make with the +x-axis? Express your answer in degrees. What angle θB, where 0 ≤ θB < 360, does B make with the +x-axis? Express your answer in degrees. Vector C is the sum of A and B, so C = A + B. What angle θC, where 0 ≤ θC <360, does C make with the +x-axis? Express your answer in degrees.

Answer 1

The angle θA that vector A makes with the +x-axis is 293.58°. The angle θB that vector B makes with the +x-axis is 18.43°. The angle θC that vector C makes with the +x-axis is 71.57°.

Step-by-step explanation:

To find the angle that vector A makes with the +x-axis, we need to find the arctan of the y-component of vector A divided by the x-component of vector A. The y-component of vector A is 7.00 and the x-component is -3.00. Therefore, the angle is arctan(7.00/-3.00) = -66.42°. However, since angles are measured counterclockwise as positive, we can add 360° to -66.42° to get 293.58° as the angle θA.

Similarly, to find the angle that vector B makes with the +x-axis, we use the arctan of the y-component of vector B divided by the x-component of vector B. The y-component of vector B is 2.00 and the x-component is 6.00. Therefore, the angle is arctan(2.00/6.00) = 18.43°.

To find the angle that vector C makes with the +x-axis, we need to find the arctan of the y-component of vector C divided by the x-component of vector C. Vector C is the sum of vectors A and B. Therefore, the y-component of vector C is the sum of the y-components of A and B (7.00 + 2.00 = 9.00), and the x-component of vector C is the sum of the x-components of A and B (-3.00 + 6.00 = 3.00). Therefore, the angle is arctan(9.00/3.00) = 71.57°.