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WAEC Further Mathematics 2011 Question 40

Question 40

Vectors

Find, correct to two decimal places, the acute angle between p = (13 / 14) and q = (12 / 5). (Column vectors written top / bottom.)

  1. A.23.52°
  2. B.24.50°
  3. C.29.52°
  4. D.29.82°
Show the answer and explanation

Answer: B (24.50°)

Explanation

p · q = 156 + 70 = 226, |p| = √365, |q| = 13. cos θ = 226/(13√365) ≈ 0.9099, so θ ≈ 24.50°.