Mathematics AI: VECTORS - LINES - PLANES Topical Past Paper Questions

[Maximum mark: 8] Air traffic control begins to monitor two airplanes. The position of the first airplane is given by $$ \boldsymbol{r}_{1}=\left(\begin{aligned}29\\ -32\\ 5.8\end{aligned}\right)+t\left(\begin{aligned}-320\\ 600\\ 0.5\end{aligned}\right), $$ where t is the time,…

[Maximum mark: 12] A national park contains three mountains whose summits are at points A, B and C. According to a coordinate system, the position of A is $ (0, 0, 2.8) $ and the position of B is $ (7.2, 5.1, 2.4) $. All the values are in kilometres. diagram not to scale (a) (i)…

[Maximum mark: 14] François is a video game designer. He designs his games to take place in two dimensions, relative to an origin O. In one of his games, an object travels on a straight line $ L_{1} $ with vector equation $$ \boldsymbol{r}=\binom{-1}{1}+\lambda\binom{2}{-1}. $$ (…