Test Index

WAEC Further Mathematics 2020 Paper

Question : 17

Total: 39

Find the angle between i + 5j and 5i - J

Solution:

Concept:

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

Explanation:

Let

\mathbf{a} = \mathbf{i} + 5\mathbf{j} = (1, 5)

and

\mathbf{b} = 5\mathbf{i} - \mathbf{j} = (5, -1)

Use

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

Compute the dot product:

\mathbf{a}\cdot\mathbf{b} = (1)(5) + (5)(-1) = 5 - 5 = 0

Find the magnitudes:

|\mathbf{a}| = \sqrt{1^2 + 5^2} = \sqrt{26}

and

|\mathbf{b}| = \sqrt{5^2 + (-1)^2} = \sqrt{26}

Therefore,

\cos\theta = \frac{0}{\sqrt{26}\sqrt{26}} = 0

So,

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

Answer:

The angle between the vectors is

90^{\circ}

Correct option: D.

90^{\circ}

Go to Question:

Prev Question

Next Question