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WAEC Further Mathematics 2016 Paper

Question : 36

Total: 40

-2i + 5j

Solution:

Concept:

A unit vector in the direction of a given vector is found by dividing the vector by its magnitude.

Explanation:

Let the vector be

\mathbf{r} = -2\mathbf{i} + 5\mathbf{j}

The magnitude is

|\mathbf{r}| = \sqrt{(-2)^2 + 5^2}

So,

|\mathbf{r}| = \sqrt{4 + 25} = \sqrt{29}

The unit vector

\hat{\mathbf{r}}

is given by

\hat{\mathbf{r}} = \frac{\mathbf{r}}{|\mathbf{r}|}

Therefore,

\hat{\mathbf{r}} = \frac{-2\mathbf{i} + 5\mathbf{j}}{\sqrt{29}}

This can be written as

\frac{1}{\sqrt{29}}(-2\mathbf{i} + 5\mathbf{j})

Answer:

\frac{1}{\sqrt{29}}(-2\mathbf{i} + 5\mathbf{j})

Correct option: B

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