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WAEC Further Mathematics 2015 Paper

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Question : 21

Total: 40

Given that

r = 2i - j

s = 3i + 5j

t = 6i - 2j

, find the magnitude of

2r + s - t

.

$\sqrt{15}$
4
$\sqrt{24}$
$\sqrt{26}$

Solution:

Concept:

Combine the given vectors using scalar multiplication and addition, then find the magnitude of the resultant vector.

Explanation:

Given:

r = 2i - j

,

s = 3i + 5j

,

t = 6i - 2j

.

First compute

2r + s - t

.

2r = 2(2i - j) = 4i - 2j

.

Now add

s

:

2r + s = (4i - 2j) + (3i + 5j) = 7i + 3j

.

Then subtract

t

:

2r + s - t = (7i + 3j) - (6i - 2j) = i + 5j

.

Magnitude of the resultant vector:

|2r + s - t| = |i + 5j| = \sqrt{1^2 + 5^2}

.

= \sqrt{1 + 25} = \sqrt{26}

.

Answer:

\sqrt{26}

Option D.

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