WAEC Further Mathematics 2012 Paper

Concept:A unit vector in the direction of a given vector is found by dividing the vector by its magnitude.Explanation:The given vector is $\vec{v} = -12\hat{i} + 5\hat{j}$.The magnitude of $\vec{v}$ gives the length of the vector:$|\vec{v}| = \sqrt{(-12)^2 + (5)^2} = \sqrt{144 + 25} = \sqrt{169} = 13$.Dividing each component by the magnitude preserves the direction and normalises the vector to length $1$.Thus, the unit vector is:$\hat{v} = \frac{\vec{v}}{|\vec{v}|} = \frac{-12\hat{i} + 5\hat{j}}{13}$.Separating the components:$\hat{v} = \frac{-12\hat{i}}{13} + \frac{5\hat{j}}{13}$.Answer:$\frac{-12\hat{i}}{13} + \frac{5\hat{j}}{13}$This matches option C.