# Thread: Vector equation for the line..

1. ## Vector equation for the line..

Find the vector equation for the line of intersection of the planes and

, ,0 8, , .

i think this problem have something to do with distance of point and plane.but that is just my guess

2. Originally Posted by DMDil
Find the vector equation for the line of intersection of the planes and

, ,0 8, , .

i think this problem have something to do with distance of point and plane.but that is just my guess
Solve the second for x, then subs. into the first and solve for y. I got

$\displaystyle x = -1 - \frac{2}{3} z,\;\;\;y = \frac{3}{2} - \frac{1}{4} z$. If we let $\displaystyle z = - 12t$

then the line is given by

$\displaystyle \bold{r} = \left(-1,\frac{3}{2},0 \right) \;+ <8,3, -12> t$

3. Originally Posted by DMDil
Find the vector equation for the line of intersection of the planes and

, ,0 8, , .

i think this problem have something to do with distance of point and plane.but that is just my guess
The point $\displaystyle (3,3,-6)$ is on both planes.
The direction vector is $\displaystyle \left\langle {3,4,3} \right\rangle \times \left\langle {3,0,2} \right\rangle$, the cross product of the normals.