Randall D. Knight — Vectors and Coordinate Systems: Problem 22

Let \(\vec{A} = (3.0\text{ m}, 20^\circ \text{ south of east})\), \(\vec{B} = (2.0\text{ m, north})\), and \(\vec{C} = (5.0\text{ m}, 70^\circ \text{ south of west})\). (a) Draw and label \(\vec{A}, \vec{B}\), and \(\vec{C}\) with their tails at the origin. Use a coordinate system with the \(x\)-axis to the east. (b) Write \(\vec{A}, \vec{B}\), and \(\vec{C}\) in component form, using unit vectors. (c) Find the magnitude and the direction of \(\vec{D} = \vec{A} + \vec{B} + \vec{C}\).