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WAEC 2020 · Paper 1 · Q37

Find the unit vector in the direction opposite to the resultant of forces F1=(−2i−3j)\mathbf{F}_1 = (-2\mathbf{i} - 3\mathbf{j}) and F2=(5i−j)\mathbf{F}_2 = (5\mathbf{i} - \mathbf{j}).

Worked solution (try it first)
  1. The resultant is F1+F2=3i−4j\mathbf{F}_1 + \mathbf{F}_2 = 3\mathbf{i} - 4\mathbf{j}.
  2. Its magnitude is 32+42=5\sqrt{3^2 + 4^2} = 5.
  3. The opposite direction is −3i+4j-3\mathbf{i} + 4\mathbf{j}.
  4. Divide by 5 to make it a unit vector: 15(−3i+4j)\frac{1}{5}(-3\mathbf{i} + 4\mathbf{j}), option B.

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