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WAEC Further Mathematics 2014 Paper

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Question : 24

Total: 40

Find the angle between

(5i + 3j)

(3i - 5j)

.

180°
90°
45°
0°

Solution:

Concept:

For two vectors,

\mathbf{a} \cdot \mathbf{b} = |\mathbf{a}||\mathbf{b}|\cos\theta

.

If the dot product is zero, the vectors are perpendicular.

Explanation:

Let

\mathbf{a} = 5\mathbf{i} + 3\mathbf{j}

and

\mathbf{b} = 3\mathbf{i} - 5\mathbf{j}

.

Compute the dot product:

\mathbf{a} \cdot \mathbf{b} = (5)(3) + (3)(-5) = 15 - 15 = 0

.

Since the numerator is zero,

\cos\theta = \frac{\mathbf{a} \cdot \mathbf{b}}{|\mathbf{a}||\mathbf{b}|} = 0

.

Thus,

\theta = \cos^{-1}(0) = 90^{\circ}

.

Answer:

90^{\circ}

(Option B).

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