# Thread: Parametric form for the straight line

1. ## Parametric form for the straight line

Check that r0 = (0, 4/3, -5/3) is a point on the intersection of the planes
3x + y - z = 3, x + 2y + 4z = -4.
Hence find a parametric form for the straight line defined by intersection of these planes.
HINT: use the fact that the line must pass through r0 and be perpendicular to the normal of each plane.

2. Hello, njr008!

(a) Check that $\displaystyle r_0 \:= \:\left(0,\:\frac{4}{3},\:-\frac{5}{3}\right)$ is a point on the intersection of the planes:

. . $\displaystyle 3x + y - z \:= \:3\;\text{ and }\;x + 2y + 4z \:=\: -4$
Substitute the coordinates into the equations of the planes
. . and show that $\displaystyle r_o$ lies on both planes.

(b) Find the parametric equations for the straight line
defined by intersection of these planes.

HINT: use the fact that the line must pass through $\displaystyle r_0$
and be perpendicular to the normal of each plane.
Find the direction vector of the line with: .$\displaystyle \langle3,1,-1\rangle \times \langle1,2,4\rangle$