Express (14 {N}, 240^{}) as a column vector.

Correct Answer is : (−7−73){-7}{-7{3}}(−73−7)

Correct Answer is : (−7−73){-7}{-7{3}}(−73−7)

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WAEC Further Mathematics 2014 Paper

Question : 40

Total: 40

Express

(14 \mathrm{N}, 240^{\circ})

Solution:

Concept:

A vector written as

(r, \theta)

can be expressed as a column vector using its horizontal and vertical components.

Explanation:

For a force

F = 14\,\mathrm{N}

at angle

\theta = 240^\circ

, the column vector is:

\binom{F\cos\theta}{F\sin\theta}

So substitute the given values:

\binom{14\cos240^\circ}{14\sin240^\circ}

Now evaluate the trigonometric ratios:

\cos240^\circ = -\frac12 \quad \text{and} \quad \sin240^\circ = -\frac{\sqrt3}{2}

Therefore:

\binom{14(-\frac12)}{14(-\frac{\sqrt3}{2})} = \binom{-7}{-7\sqrt3}

Answer:

\binom{-7}{-7\sqrt3}

This is option A.

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