Given: Force F = (4i − 7j − 4k)N acts at position vector r_A = (3i + 4j − 6k)m.

Let's solve these Further Mathematics questions.

1. Force and Vectors

Given: Force $\mathbf{F} = (4\mathbf{i} - 7\mathbf{j} - 4\mathbf{k})\text{N}$ acts at position vector $\mathbf{r}_A = (3\mathbf{i} + 4\mathbf{j} - 6\mathbf{k})\text{m}$.

• 1 (i) Write down a vector equation of the line of action of F.

Step 1: Identify a point on the line and the direction vector.
The line of action passes through the point where the force acts, $\mathbf{r}_A = 3\mathbf{