Find the direction cosines of the vector \(4i - 3j\).
FURTHER MATHEMATICS
WAEC 2010
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. \(\frac{4}{7}, \frac{-3}{7}\)
Correct Answer: C. \(\frac{4}{5}, -\frac{3}{5}\)
Explanation
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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