Halliday, Resnick & Walker — Vectors: Problem 48

Two vectors \(\vec{a}\) and \(\vec{b}\) have the components, in meters, \(a_x = 3.2, a_y = 1.6, b_x = 0.50, b_y = 4.5\). (a) Find the angle between the directions of \(\vec{a}\) and \(\vec{b}\). There are two vectors in the \(xy\) plane that are perpendicular to \(\vec{a}\) and have a magnitude of 5.0 m. One, vector \(\vec{c}\), has a positive \(x\) component and the other, vector \(\vec{d}\), a negative \(x\) component. What are (b) the \(x\) component and (c) the \(y\) component of vector \(\vec{c}\), and (d) the \(x\) component and (e) the \(y\) component of vector \(\vec{d}\)?