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Find the unit vector in the direction of the vector \(-12i + 5j\).

Further Mathematics
WAEC 2012

Find the unit vector in the direction of the vector \(-12i + 5j\).

  • A. \(\frac{-12i}{13} - \frac{5j}{13}\)
  • B. \(\frac{-1i}{13} + \frac{5j}{13}\)
  • C. \(\frac{-12i}{13} + \frac{5j}{13}\)
  • D. \(\frac{-5i}{13} + \frac{12j}{13}\)
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Correct Answer: Option C
Explanation

\(\hat{n} = \frac{\overrightarrow{n}}{|n|}\)

\(\hat{n} = \frac{-12i + 5j}{\sqrt{(-12)^{2} + (5)^{2}}}\)

= \(\frac{-12i}{13} + \frac{5j}{13}\)


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