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WAEC Further Mathematics 2011 Question 37

Question 37

Vectors

Given that q = 9i + 6j and r = 4i − 6j, which of the following statements is true?

  1. A.r and q are collinear
  2. B.r and q are perpendicular
  3. C.The magnitude of r is 52 units
  4. D.The projection of r on q is √117 units
Show the answer and explanation

Answer: B (r and q are perpendicular)

Explanation

q · r = 9 × 4 + 6 × (−6) = 36 − 36 = 0. A zero dot product means the vectors are perpendicular.