Find the direction cosines of the vector \(4i - 3j\).

  • A \(\frac{9}{10}, \frac{27}{10}\)
  • B \(\frac{17}{27}, -\frac{17}{27}\)
  • C \(\frac{4}{5}, -\frac{3}{5}\)
  • D \(\frac{4}{7}, \frac{-3}{7}\)
waec 2010furthermathematics

The correct answer is C. \(\frac{4}{5}, -\frac{3}{5}\)

Given \(V = xi +yj\), the direction cosines are \(\frac{x}{|V|}, \frac{y}{|V|}\).

\(|4i - 3j| = \sqrt{4^{2} + (-3)^{2}} = \sqrt{25} = 5\)

Direction cosines = \(\frac{4}{5}, \frac{-3}{5}\).

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