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Given that \(p = 4i + 3j\), find the unit vector in the direction of...

Further Mathematics
WAEC 2007

Given that \(p = 4i + 3j\), find the unit vector in the direction of p.

  • A. \(\frac{1}{3}(4i + 3j)\)
  • B. \(\frac{1}{3}(3i + 4j)\)
  • C. \(\frac{1}{5}(3i + 4j)\)
  • D. \(\frac{1}{5}(4i + 3j)\)
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Correct Answer: Option D
Explanation

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

where \(\hat {n}\) is the unit vector in the direction of p.

\(|p| = \sqrt{4^{2} + 3^{2}} = \sqrt{25} = 5\)

\(\hat {n} = \frac{1}{5} (4i + 3j)\)


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