I have a plane V with cartesian equation 2x−y+3z=10. I also have a line that is perpendicular to the plane V with parametric equation (x,y,z)=(1,0,−2)+(2,−1,3)t. How do I find the point of intersection between the line and plane?

erkentrs

erkentrs

Open question

2022-08-17

I have a plane V with cartesian equation 2x−y+3z=10. I also have a line that is perpendicular to the plane V with parametric equation (x,y,z)=(1,0,−2)+(2,−1,3)t.
How do I find the point of intersection between the line and plane?

Answer & Explanation

Kobe Ortiz

Kobe Ortiz

Beginner2022-08-18Added 9 answers

Hint: Plug
x=1+2t
y=−t
z=−2+3t
in the equation for the plane and compute t

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