Relative to the origin $O$, the position vectors of points $A$, $B$ and $C$ are $\mathbf{a}$, $\mathbf{b}$ and $\mathbf{c}$ respectively. It is given that&nbsp;$\left| \mathbf{a} \right|=\sqrt{3}$ and $\left| \mathbf{c} \right|=4$, and the angle between $\mathbf{a}$ and $\mathbf{c}$ is $60{}^\circ $
Given that&nbsp;$\mathbf{a}\times 2\mathbf{b}=3\mathbf{a}\times \mathbf{c}$, and $3\mathbf{b}\times \mathbf{c}=\mathbf{c}\times 4\mathbf{a}$, show that
$\left| \overrightarrow{AB}\times \overrightarrow{AC} \right|=k\left| \mathbf{a}\times \mathbf{c} \right|$
where&nbsp;$k$ is a constant to be determined.[4]
Hence find the exact area of triangle $ABC$.[2]

Relative to the origin $O$, the position vectors of points $A$, $B$ and $C$ are $\mathbf{a}$, $\mathbf{b}$ and $\mathbf{c}$ respectively. It is given that $\left| \mathbf{a} \right|=\sqrt{3}$ and $\left| \mathbf{c} \right|=4$, and the angle between $\mathbf{a}$ and $\mathbf{c}$ is $60{}^\circ $

Given that $\mathbf{a}\times 2\mathbf{b}=3\mathbf{a}\times \mathbf{c}$, and $3\mathbf{b}\times \mathbf{c}=\mathbf{c}\times 4\mathbf{a}$, show that

$\left| \overrightarrow{AB}\times \overrightarrow{AC} \right|=k\left| \mathbf{a}\times \mathbf{c} \right|$

where $k$ is a constant to be determined.

Hence find the exact area of triangle $ABC$.

Vectors - General

Vectors

H2 Math

International Baccalaureate Higher Level Mathematics

2020 HCI Promo Q5

2020 HCI Promo Q5

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