Moderate -0.8 This is a straightforward application of the work done formula W = F·d, requiring only calculation of the displacement vector AB and then a dot product. It's a standard M5 question testing basic recall of the work-energy principle with no problem-solving or conceptual challenges beyond routine vector arithmetic.
A particle moves from the point \(A\) with position vector \((3\mathbf{i} - \mathbf{j} + 3\mathbf{k})\) m to the point \(B\) with position vector \((\mathbf{i} - 2\mathbf{j} - 4\mathbf{k})\) m under the action of the force \((2\mathbf{i} - 3\mathbf{j} - \mathbf{k})\) N. Find the work done by the force.
[4]
A particle moves from the point $A$ with position vector $(3\mathbf{i} - \mathbf{j} + 3\mathbf{k})$ m to the point $B$ with position vector $(\mathbf{i} - 2\mathbf{j} - 4\mathbf{k})$ m under the action of the force $(2\mathbf{i} - 3\mathbf{j} - \mathbf{k})$ N. Find the work done by the force.
[4]
\hfill \mbox{\textit{Edexcel M5 2011 Q1 [4]}}