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WAEC Further Mathematics 2013 Paper

Question : 29

Total: 40

s = 3i - j

t = 2i + 3j

(t - 3s).(t + 3s)

Solution:

Concept:

Simplifying vector expressions before applying the dot product.

Explanation:

Start by substituting the given vectors

s = 3i - j

and

t = 2i + 3j

into each bracket.

First, calculate

t - 3s

(2i + 3j) - 3(3i - j) = 2i + 3j - 9i + 3j = -7i + 6j

Next, calculate

t + 3s

(2i + 3j) + 3(3i - j) = 2i + 3j + 9i - 3j = 11i

Now apply the dot product to the simplified vectors:

(-7i + 6j) \cdot (11i)

Use

i \cdot i = 1

and

j \cdot i = 0

= (-7)(11) + (6)(0) = -77

The dot product of the given expressions is

-77

Answer:

A. -77

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