Applications of vectors to 3-D geometryEdexcel A-Level Further Maths: Mind map

Exam questions on Applications of vectors to 3-D geometry

1. The line $l$ has vector equation $\mathbf{r}=(\mathbf{i}-2\mathbf{j}+3\mathbf{k})+\lambda(2\mathbf{i}+\mathbf{j}-2\mathbf{k})$.
   Find Cartesian equations for $l$.2 marks
2. The plane $\Pi$ passes through the point $A(1,2,3)$ and is perpendicular to the vector $2\mathbf{i}-\mathbf{j}+2\mathbf{k}$.
   The line $m$ passes through the origin and has direction $\mathbf{i}+\mathbf{j}+\mathbf{k}$. Find the coordinates of the point where $m$ meets $\Pi$.2 marks
3. The line $l$ has Cartesian equation $\frac{x-1}{3}=\frac{y+2}{-4}=\frac{z}{12}$, and the point $P$ has coordinates $(5,1,0)$.
   Find the direction cosines of $l$, and the acute angle that $l$ makes with the $z$-axis.3 marks