WAEC Further Mathematics 2017 Paper

Concept:Find the magnitude using Pythagoras' theorem, then use the ratio of the components to get the direction.Explanation:Given $p = 5i - 12j$.The horizontal component is $5$ and the vertical component is $-12$.Magnitude:$|p| = \sqrt{5^2 + (-12)^2}$$= \sqrt{25 + 144}$$= \sqrt{169}$$= 13$.Now, find the acute angle with the horizontal:$\tan \gamma = \frac{12}{5}$So, $\gamma = 67.38^\circ$.The vector points $67.38^\circ$ below the positive $x$-axis.Measured from the positive $y$-axis, its direction is:$90^\circ + 67.38^\circ = 157.38^\circ$.Answer:D. $(13, 157.38^\circ)$