Find the unit vector in the direction opposite to the resultant of forces. F\(_1\) =
FURTHER MATHEMATICS
WAEC 2020
Find the unit vector in the direction opposite to the resultant of forces. F\(_1\) = (-2i - 3j) and F\(_2\) = (5i - j)
- A. \(\frac{1}{5}\)(-3i - 4j)
- B. \(\frac{1}{5}\)(-3i + 4j)
- C. \(\frac{1}{5}\)(3i - 4j)
- D. \(\frac{1}{5}\)(3i + 4j)
Correct Answer: C. \(\frac{1}{5}\)(3i - 4j)
Explanation
Resultant
(- 2i - 3j) + (5i - j)
= 3i - 4j
Unit vector
= \(\frac{3i - 4j}{|3i - 4j|} = \frac{3i - 4j}{\sqrt{3i } + (-4)}\)
= \(\frac{3i - 4j}{\sqrt{25}}\)
= \(\frac{3i - 4j}{5}\)
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