Given that \(a = i - 3j\) and \(b = -2i + 5j\) and \(c = 3i - j\), calculate \(|a - b + c|\).

  • A \(\sqrt{13}\)
  • B \(3\sqrt{13}\)
  • C \(6\sqrt{13}\)
  • D \(9\sqrt{13}\)
waec 2018furthermathematics

The correct answer is B. \(3\sqrt{13}\)

Given \(a = i - 3j; b = -2i + 5j; c = 3i - j\)

\(a- b + c = (1 - (-2) + 3)i + (-3 - 5 + (-1))j = 6i - 9j\)

\(|a - b + c| = \sqrt{6^{2} + (-9)^{2}} = \sqrt{36 + 81} = \sqrt{117}\)

\(= \sqrt{9 \times 13} = 3\sqrt{13}\)

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