Vector and Cartesian equations of linesAQA A-Level Further Maths: Mind map

Exam questions on Vector and Cartesian equations of lines

1. The line $l$ passes through the points $A(1,2,-1)$ and $B(3,-2,3)$.
   Show that the point $C(5,-6,7)$ lies on $l$.2 marks
2. A line $l_1$ has Cartesian equation $\frac{x-2}{3}=\frac{y+1}{-2}=\frac{z-4}{5}$.
   Find the coordinates of the point on $l_1$ at which $z=-1$.2 marks
3. The line $l_2$ has vector equation $\mathbf r=\begin{pmatrix} 4 \\ -3 \\ 1 \end{pmatrix}+\mu\begin{pmatrix} 2 \\ -1 \\ 3 \end{pmatrix}$.
   Find a Cartesian equation of $l_2$.3 marks