What is the angle between \(a = (3i - 4j)\) and \(b = (6i +
FURTHER MATHEMATICS
WAEC 2010
What is the angle between \(a = (3i - 4j)\) and \(b = (6i + 4j)\)?
- A. 13°
- B. 87°
- C. 100°
- D. 110°
Correct Answer: B. 87°
Explanation
\(a . b = |a||b| \cos \theta\)
\(a = 3i - 4j; b = 6i + 4j\)
\(18 - 16 = (\sqrt{3^{2} + (-4)^{2}})(\sqrt{6^{2} + 4^{2}}) \cos \theta\)
\(2 = 5\sqrt{52} \cos \theta\)
\(\cos \theta = \frac{2}{5\sqrt{52}} = 0.0555\)
\(\theta = 86.8° \approxeq 87°\)
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