# Thread: point where Plane P intersects

1. ## point where Plane P intersects

i don't know why i am not getting this material like i should, anyway,, i am stuck here..
A Plane P is orthogonal(perpendicular) to the line L: x=4+2t, y=-1+3t, z=2+t and passes through the point A =(4, 1,7) Find the point where the plane P intersets the x-axis.
(Hint: Find the equation of the plane P)

Answer: ( , , )

also tell me how can i better understand parallel, orthogonal and skew stuff on line and plane

2. Originally Posted by DMDil
i don't know why i am not getting this material like i should, anyway,, i am stuck here..
A Plane P is orthogonal(perpendicular) to the line L: x=4+2t, y=-1+3t, z=s+t and passes through the point A =(4, 1,7) Find the point where the plane P intersets the x-axis.
First note that the red above must be a typo.
The direction of the line is the normal of the plane if the line is perpendicular to the plane.
Thus the plane is $2(x-4)+3(y-1)+(z-7)=0$.
Substitute the parametric forms for x, y, & z. Then solve for t.

3. Originally Posted by DMDil
... Find the point where the plane P intersets the x-axis.
(Hint: Find the equation of the plane P)

...
Take Plato's equation of the plane. Keep in mind that a point on the x-axis has the coordinates (c, 0, 0). Plug in these coordinates into the equation of the plane and solve for c.

I've got $C(9, 0, 0)$

4. oops sorry, it was z=2+t