Question
Bahasa Melayu
Rajah 1 menunjukkan trapezium $ABCD$ dengan keadaan $AD$ selari dengan $BC$. Titik $N$ terletak pada garis lurus $BD$. Diberi bahawa $\vec{AD} = 12q$, $\vec{AB} = 6p$, $AD : BC = 3 : 1$ dan $BN : BD = 1 : 4$, dengan keadaan $p$ dan $q$ ialah vektor tak sifar yang tidak selari antara satu sama lain. Diberi juga bahawa $\vec{AC} = 6p + 4q$.
Titik $N$ memenuhi $\vec{AN} = h\,\vec{AC}$. Cari nilai $h$.
Titik $N$ memenuhi $\vec{AN} = h\,\vec{AC}$. Cari nilai $h$.
English
Diagram 1 shows trapezium $ABCD$ in which $AD$ is parallel to $BC$. The point $N$ lies on the straight line $BD$. It is given that $\vec{AD} = 12q$, $\vec{AB} = 6p$, $AD : BC = 3 : 1$ and $BN : BD = 1 : 4$, where $p$ and $q$ are non-zero vectors that are not parallel to each other. It is also given that $\vec{AC} = 6p + 4q$.
The point $N$ satisfies $\vec{AN} = h\,\vec{AC}$. Find the value of $h$.
The point $N$ satisfies $\vec{AN} = h\,\vec{AC}$. Find the value of $h$.
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Modelled on SBP trial · Kertas 2 · Q1(b)
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Modelled on SBP trial · Kertas 2 · Q1(b)
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