Referred to the origin $O$, points $A$ and $B$ have position vectors $\mathbf{a}$ and $\mathbf{b}$ r

Question

Referred to the origin $O$, points $A$ and $B$ have position vectors $\mathbf{a}$ and $\mathbf{b}$ respectively. Point $C$ lies on $AB$ produced such that $BC:AC=3:5$. Find the position vector of point $C$, giving your answer in terms of $\mathbf{a}$ and $\mathbf{b}$. [2] $\mathbf{p}$ is a given vector such that $\mathbf{b}\cdot \mathbf{p}=-2$ and $\overrightarrow{OC}\cdot \mathbf{p}=-5$. Find the value of $\mathbf{a}\cdot \mathbf{p}$ and state the geometrical relationship between $\mathbf{a}$ and $\mathbf{p}$. [3] The vertices of a triangle have position vectors $\mathbf{i}+\mathbf{j}+\mathbf{k}$, $3\mathbf{i}+4\mathbf{j}+2\mathbf{k}$ and $\mathbf{i}+t\mathbf{j}-t\mathbf{k}$ respectively, where $t$ is an unknown constant. Given that the triangle has area $\sqrt{19}$, find the possible value(s) of $t$. [4]

Accepted Answer

(a)(i) OC = (5b-3a)/2; (a)(ii) a ⊥ p; (b) t = 4/3 or t = -2

2022 EJC J1 MYE Q5

2022 EJC J1 MYE Q5

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