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WAEC Further Mathematics 2024 Paper

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Question : 14

Total: 40

If r = i + 2j and n = -i + 3j, find |2n - r|.

3.6
4.0
5.0
8.5

Solution:

Concept:

Use vector algebra to find the resultant vector, then apply the magnitude formula.

Explanation:

Given

\mathbf{r} = \mathbf{i} + 2\mathbf{j}

and

\mathbf{n} = -\mathbf{i} + 3\mathbf{j}

.

First, compute

2\mathbf{n}

:

2\mathbf{n} = 2(-\mathbf{i} + 3\mathbf{j}) = -2\mathbf{i} + 6\mathbf{j}

.

Now, subtract

\mathbf{r}

from

2\mathbf{n}

:

2\mathbf{n} - \mathbf{r} = (-2\mathbf{i} + 6\mathbf{j}) - (\mathbf{i} + 2\mathbf{j})

.

Simplify component-wise:

= (-2 - 1)\mathbf{i} + (6 - 2)\mathbf{j} = -3\mathbf{i} + 4\mathbf{j}

.

Find the magnitude:

|2\mathbf{n} - \mathbf{r}| = \sqrt{(-3)^2 + 4^2}

.

= \sqrt{9 + 16} = \sqrt{25} = 5.0

.

Answer:

5.0

(Option C).

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