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Express \(r = (12, 210°)\) in the form \(a i + b j\).

Further Mathematics
WAEC 2008

Express \(r = (12, 210°)\) in the form \(a i + b j\).

  • A. \(6(-i + \sqrt{3} j)\)
  • B. \(6(-\sqrt{3} i - j)\)
  • C. \(6(i - \sqrt{3} j)\)
  • D. \(6(i + \sqrt{3} j)\)
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Correct Answer: Option B
Explanation

\(F = F \cos \theta i + F \sin \theta j\)

\(r = (12, 210°) = 12 \cos 210 i + 12 \sin 210 j\)

= \(- 6\sqrt{3} i - 6j\)

= \(6(-\sqrt{3} i - j)\)


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