Given that AB={4}{2} and AC={2}{2}, find IBCl .

Correct Answer is : 2102{10}210

Correct Answer is : 2102{10}210

Test Index

WAEC Further Mathematics 2014 Paper

Question : 23

Total: 40

Given that

AB=\binom{4}{2}

AC=\binom{2}{2}

, find IBCl .

Solution:

Concept:

Use the triangle law of vector addition.

The displacement from

B

C

equals going from

B

A

, then from

A

C

Explanation:

\overrightarrow{BC} = \overrightarrow{BA} + \overrightarrow{AC}

Since

\overrightarrow{BA} = -\overrightarrow{AB}

, we reverse the given vector.

Given

\overrightarrow{AB} = \binom{4}{3}

, we get:

\overrightarrow{BA} = -\binom{4}{3} = \binom{-4}{-3}

Now add

\overrightarrow{AC} = \binom{2}{-3}

\overrightarrow{BC} = \binom{-4}{-3} + \binom{2}{-3} = \binom{-2}{-6}

Find the magnitude:

|\overrightarrow{BC}| = \sqrt{(-2)^2 + (-6)^2} = \sqrt{4 + 36} = \sqrt{40}

Simplify:

\sqrt{40} = 2\sqrt{10}

This matches option C.

Answer:

2\sqrt{10}

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