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WAEC Further Mathematics 2010 Paper

Question : 40

Total: 40

a = (3i - 4j)

b = (6i + 4j)

Solution:

Concept:

The angle between two vectors is found using the dot product formula:

Explanation:

For vectors

a

and

b

, the dot product formula is:

a \cdot b = |a||b|\cos\theta

Given

a = 3i - 4j

and

b = 6i + 4j

Compute the dot product:

a \cdot b = (3)(6) + (-4)(4) = 18 - 16 = 2

Compute the magnitudes:

|a| = \sqrt{3^2 + (-4)^2} = \sqrt{25} = 5

|b| = \sqrt{6^2 + 4^2} = \sqrt{36 + 16} = \sqrt{52}

Substitute into the formula:

2 = 5\sqrt{52}\cos\theta

\cos\theta = \frac{2}{5\sqrt{52}} \approx 0.0555

\theta = \cos^{-1}(0.0555) \approx 86.8^{\circ}

\theta \approx 87^{\circ}

Answer:

B. 87°

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