# Thread: parametric equations, equations of plane

1. ## parametric equations, equations of plane

Find the parametric equations of the line through (5, -3, 4) that intersects the z-axis at a right angle.
what do i do, since it says right angle?

Show that the lines (x-1)/-4 = (y-2)/3 = (z-4)/-2 and (x-2)/-1 = (y-1)/1 = (z+2)/6 intersect, and find the equation of the plane that they determine.
how would you do this??

2. Hi Arez

Question 1
You need to find the direction vector of the line that is perpendicular to z-axis.
Any random vectors $\displaystyle \left(\begin{array}{c}x\\y\\z\end{array}\right)$ will be perpendicular to z-axis if the z-component is zero. Because the line passes through (5, -3, 4), it will have direction vector $\displaystyle \left(\begin{array}{c}5\\-3\\0\end{array}\right)$

There is other method but I think maybe this is the fastest one.

Question 2
Those two are Cartessian form of line equation. Have you learned how to change them to vector form of line equation?