Okay, let's solve this step-by-step:
1) Given:
A → = 2.0 x ^ − 3.2 y ^
B → = − 1.2 x ^ + 2.9 y ^
Find: Angle between D → = A → − B → and positive x-axis
2) Subtract the vectors to find D →:
D → = 2.0 x ^ − 3.2 y ^ - (− 1.2 x ^ + 2.9 y ^ )
= 2.0 x ^ − 3.2 y ^ + 1.2 x ^ - 2.9 y ^
= 3.2 x ^ − 6.1 y ^
3) To find the angle, we use the inverse tangent ratio of y/x:
Angle = tan−1(−6.1/3.2) = -61.97°
4) Since the angle is in the 4th quadrant, it is measured clockwise from the positive x-axis. So the final angle is 180 - 61.97 = 118.03°
Therefore, the angle between the vector D → = A → − B → and the positive x-axis is 118.03°.
Let me know if you have any other questions!