Matematik Tambahan SPM 2017, Kertas 1 (Soalan 1 – 3)

Soalan 3 (3 markah):
Rajah 3 menunjukkan vektor-vektor $\overrightarrow{AB},\overrightarrow{AC}\text{ dan }\overrightarrow{AD}$ yang dilukis pada grid segi empat sama bersisi 1 unit.

Rajah 3

$\begin{array}{l}\left(\text{a}\right)\text{ Cari }\left|-\overrightarrow{BA}\right|.\\ \left(\text{b}\right)\text{ Diberi }\overrightarrow{AB}=\underset{˜}{b}\text{ dan }\overrightarrow{AC}=\underset{˜}{c},\\ \text{ungkapkan dalam sebutan }\underset{˜}{b}\text{ dan }\underset{˜}{c}\\ \left(i\right)\overrightarrow{BC},\\ \left(ii\right)\overrightarrow{AD}\end{array}$


Penyelesaian:
(a)
$\left|-\overrightarrow{BA}\right|=\sqrt{3^2+4^2}=5\text{ unit}$

(b)(i)
$\begin{array}{l}\overrightarrow{BC}=\overrightarrow{BA}+\overrightarrow{AC}\\ =-\underset{˜}{b}+\underset{˜}{c}\\ =\underset{˜}{c}-\underset{˜}{b}\end{array}$

(b)(ii)
$\begin{array}{l}\overrightarrow{AD}=\overrightarrow{AB}+\overrightarrow{BD}\\ =\underset{˜}{b}+2\overrightarrow{BC}\\ =\underset{˜}{b}+2\left(\underset{˜}{c}-\underset{˜}{b}\right)\\ =2\underset{˜}{c}-\underset{˜}{b}\end{array}$