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WAEC Further Mathematics 2018 Paper

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Question : 32

Total: 40

Given that

a = \hat{i} - 3\hat{j}

b = -2\hat{i} + 5\hat{j}

c = 3\hat{i} - \hat{j}

\left| a - b + c \right|

.

$\sqrt{13}$
$3\sqrt{13}$
$6\sqrt{13}$
$9\sqrt{13}$

Solution:

Concept:

Vector addition/subtraction and magnitude of a resultant vector.

Explanation:

Given:

a = \hat{i} - 3\hat{j}

,

b = -2\hat{i} + 5\hat{j}

,

c = 3\hat{i} - \hat{j}

.

First find

a - b + c

.

Coefficient of

\hat{i}

:

1 - (-2) + 3 = 6

.

Coefficient of

\hat{j}

:

-3 - 5 + (-1) = -9

.

So

a - b + c = 6\hat{i} - 9\hat{j}

.

Now compute the magnitude:

\left| a - b + c \right| = \sqrt{6^2 + (-9)^2} = \sqrt{36 + 81} = \sqrt{117}

.

Simplify:

\sqrt{117} = \sqrt{9 \times 13} = 3\sqrt{13}

.

Answer:

3\sqrt{13}

, which is option B.

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