Find the unit vector in the direction of \(-2i + 5j\).
FURTHER MATHEMATICS
WAEC 2016
Find the unit vector in the direction of \(-2i + 5j\).
- A. \(\frac{1}{\sqrt{29}}(2i + 5j)\)
- B. \(\frac{1}{\sqrt{29}}(-2i + 5j)\)
- C. \(\frac{1}{29}(2i - 5j)\)
- D. \(\frac{1}{29}(-2i - 5j)\)
Correct Answer: B. \(\frac{1}{\sqrt{29}}(-2i + 5j)\)
Explanation
The unit vector, \(\hat{n}\) is given by \(\hat{n} = \frac{\overrightarrow{r}}{|\overrightarrow{r}|}\)
= \(\frac{(-2i + 5j)}{\sqrt{(-2)^{2} + 5^{2}}} = \frac{(-2i + 5j)}{\sqrt{29}}\)
= \(\frac{1}{\sqrt{29}}(-2i + 5j)\)
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