Moderate -0.8 This is a straightforward vector addition problem requiring students to sum three given vectors, calculate the magnitude using Pythagoras, and find direction using arctangent. It's a standard textbook exercise with clear steps: add components, apply √(x²+y²), then tan⁻¹(y/x). The arithmetic is simple and the method is routine, making it easier than average.
Three forces \(\mathbf{L}\), \(\mathbf{M}\) and \(\mathbf{N}\) are given by
$$\mathbf{L} = 2\mathbf{i} + 5\mathbf{j},$$
$$\mathbf{M} = 3\mathbf{i} - 22\mathbf{j},$$
$$\mathbf{N} = 4\mathbf{i} - 23\mathbf{j}.$$
Find the magnitude and direction of the resultant of the three forces. [6]
Three forces $\mathbf{L}$, $\mathbf{M}$ and $\mathbf{N}$ are given by
$$\mathbf{L} = 2\mathbf{i} + 5\mathbf{j},$$
$$\mathbf{M} = 3\mathbf{i} - 22\mathbf{j},$$
$$\mathbf{N} = 4\mathbf{i} - 23\mathbf{j}.$$
Find the magnitude and direction of the resultant of the three forces. [6]
\hfill \mbox{\textit{WJEC Unit 2 2018 Q09 [6]}}