1. ## calculus

Determine the parametric equations for the line that passes through the two points A=(4, -1, 5) and B= (3, 5, -1).
At what point does this line intersect the x-y plane

2. Originally Posted by tob2dam
Determine the parametric equations for the line that passes through the two points A=(4, -1, 5) and B= (3, 5, -1).
At what point does this line intersect the x-y plane

As you know a line equation in $\mathrm{R}^{3}$ has the following form:
$\alpha(t):=A+tu,\qquad t\in\mathbb{R},$
where $A$ is a point that line passes through, and $u\neq(0,0,0)$ is a vector that is parallel to the line.
Returning to your problem, we have a point that the desired line passes through (we may pick $(4, -1, 5)$ or $(3, 5, -1)$), but we need the vector $u$.
We may let $u$ as $AB$ vector, try to see that the line will be parallel to $AB=B-A=(-1,6,-6)$.
Thus, the line is
$\alpha(t):=(4,-1,5)+t(-1,6,-6),\qquad t\in\mathbb{R}.$
To find the value that line intersects $xy$-plane, we have to set the third component (height) of the line to $0$ and solve $t$.
I hope you can find it now?