WAEC 2020 · Paper 1 · Q19

Statics: forces, equilibrium & moments
Vectors

Given that $\mathbf{F} = 3\mathbf{i} - 12\mathbf{j}$ , $\mathbf{R} = 7\mathbf{i} + 5\mathbf{j}$ and $\mathbf{N} = p\mathbf{i} + q\mathbf{j}$ are forces acting on a body, if the body is in equilibrium, find the values of $p$ and $q$ .

Worked solution (try it first)

In equilibrium the forces add up to zero: $\mathbf{F} + \mathbf{R} + \mathbf{N} = \mathbf{0}$ .
$\mathbf{i}$ parts: $3 + 7 + p = 0$ , so $p = -10$ .
$\mathbf{j}$ parts: $-12 + 5 + q = 0$ , so $q = 7$ .
So $p = -10, q = 7$ , option A.

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