The points $P$, $Q$, and $R$ have position vectors given by $\mathbf{i}-\mathbf{j}-\mathbf{k}$, $\ma

Question

The points $P$, $Q$, and $R$ have position vectors given by $\mathbf{i}-\mathbf{j}-\mathbf{k}$, $\mathbf{i}+3\mathbf{j}+\mathbf{k}$ and $\left( 2-2t \right)\mathbf{i}+\left( 1+4t \right)\mathbf{j}+\left( 3-4t \right)\mathbf{k}$ respectively. Find angle $OPQ$. [3] Find the exact area of triangle $OPQ$. [3] Find the values of $t$ such that the length of the projection of $\overrightarrow{PR}$ onto $\overrightarrow{PQ}$ is $\sqrt{5}$ units. [4]

Accepted Answer

(i) $39.2^\circ$; (ii) $\sqrt6$ units²; (iii) $t=-\frac34$ or $-\frac{13}4$.

2022 TJC J1 MYE Q5

2022 TJC J1 MYE Q5

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