# Thread: question distance between vector planes

1. ## question distance between vector planes

Hi

My question is

Distance $\ell$of the point $\overrightarrow{P}$from the line $\overrightarrow{r}=\overrightarrow{r_{0}}+t\overri ghtarrow{v}$ can be calculated as $\ell=\frac{\left|(\overrightarrow{P}-\overrightarrow{r_{0}})\times\overrightarrow{v}\ri ght|}{\left|\overrightarrow{v}\right|}$

Find how far is the point (4,1,1) from the line where the two planes $x+2y=4$and $y=0$intersect.

2. Note y= 0 is the xz plane

we have then x= 4 in the x-z plane

we can parameterize the line of intersection x= 4

y= 0

z = t

r = 4i + t k r0 = 4i