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WAEC Further Mathematics 2011 Paper

Question : 39

Total: 40

Find the unit vector in the direction of (-5i + 12j).

Solution:

Concept:

The unit vector in a given direction is obtained by dividing the vector by its magnitude.

Explanation:

Let

\vec{r} = -5\mathbf{i} + 12\mathbf{j}

First, find the magnitude:

|\vec{r}| = \sqrt{(-5)^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169} = 13

The unit vector is

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

Thus,

\hat{r} = \frac{-5\mathbf{i} + 12\mathbf{j}}{13} = \frac{1}{13}(-5\mathbf{i} + 12\mathbf{j})

Answer:

\frac{1}{13}(-5\mathbf{i} + 12\mathbf{j})

, which is option C.

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