WAEC Further Mathematics 2013 Paper

Concept:For two vectors written as column vectors, add their corresponding components to find the resultant vector, then use Pythagoras to find its magnitude.Explanation:Given vectors are $U = \binom{-1}{5}$ and $V = \binom{-2}{4}$.Add the vectors component-wise:$$U + V = \binom{-1 + (-2)}{5 + 4} = \binom{-3}{9}$$The expression $|U + V|$ means the magnitude of the resultant vector.Magnitude is found using:$$|U + V| = \sqrt{(-3)^2 + 9^2}$$$$= \sqrt{9 + 81} = \sqrt{90}$$Simplify $\sqrt{90}$:$$\sqrt{90} = \sqrt{9 \times 10} = 3\sqrt{10}$$This matches option A.Answer:$3\sqrt{10}$ (Option A)