SPM Additional Mathematics 2017, Paper 1 (Question 1 - 3)

Question 3 (3 marks):
Diagram 3 shows vectors

\vec{A B}, \vec{A C} and \vec{A D}

drawn on a square grid with sides of 1 unit.

Diagram 3

\begin{array}{l} (a) Find | - \vec{B A} | . \\ (b) Given \vec{A B} = \underset{˜}{b} and \vec{A C} = \underset{˜}{c}, \\ express in terms of \underset{˜}{b} and \underset{˜}{c} \\ (i) \vec{B C}, \\ (i i) \vec{A D} \end{array}

Solution:
(a)

| - \vec{B A} | = \sqrt{3^{2} + 4^{2}} = 5 units

(b)(i)

\begin{array}{l} \vec{B C} = \vec{B A} + \vec{A C} \\ = - \underset{˜}{b} + \underset{˜}{c} \\ = \underset{˜}{c} - \underset{˜}{b} \end{array}

(b)(ii)

\begin{array}{l} \vec{A D} = \vec{A B} + \vec{B D} \\ = \underset{˜}{b} + 2 \vec{B C} \\ = \underset{˜}{b} + 2 (\underset{˜}{c} - \underset{˜}{b}) \\ = 2 \underset{˜}{c} - \underset{˜}{b} \end{array}

SPM Additional Mathematics 2017, Paper 1 (Question 1 – 3)