Vector equations of linesEdexcel International A Level Maths: Mind map

Exam questions on Vector equations of lines

1. The line $l_1$ passes through the points $A(2,-1,3)$ and $B(5,1,1)$.
   Find the coordinates of the point where $l_1$ crosses the plane $z=0$.2 marks
2. The line $m$ passes through the points $C(1,4,-2)$ and $D(3,3,0)$.
   Determine whether the point $E(-3,6,-6)$ lies on $m$.2 marks
3. Line $l_1$ has equation $\mathbf{r}=(\mathbf{i}+\mathbf{j}+2\mathbf{k})+s(2\mathbf{i}+\mathbf{j}-\mathbf{k})$ and line $l_2$ has equation $\mathbf{r}=(\mathbf{i}+4\mathbf{j}+5\mathbf{k})+t(\mathbf{i}-\mathbf{j}-2\mathbf{k})$, where $s$ and $t$ are scalar parameters.
   Show that $l_1$ and $l_2$ intersect, and find the coordinates of the point of intersection.3 marks