Finding if vector line doesn't cross 3D plane v = (2i − 3j + k) + µ(i − 2j) + ν(i + k

[pkusy882]

Finding if vector line doesn't cross 3D plane v = (2i − 3j + k) + µ(i − 2j) + ν(i + k

Hi everyone,

Let P be the plane with equationv = (2i − 3j + k) + µ(i − 2j) + ν(i + k).

(b) Where does the line with equationv = (5i + 6j) + λ(2j + k) meet the plane P?

I was facing difficulties answering this as the answer was that it did not cross anywhere. I am unsure how to show that the line does not cross the plane.

 

[Deleted member 4993]

Hi everyone,

Let P be the plane with equationv = (2i − 3j + k) + µ(i − 2j) + ν(i + k).

(b) Where does the line with equationv = (5i + 6j) + λ(2j + k) meet the plane P?

I was facing difficulties answering this as the answer was that it did not cross anywhere. I am unsure how to show that the line does not cross the plane.

The given line must be perpendicular to the normal to the plane.

 

[pkusy882]

Thanks for replying so quickly.
If that line is perpendicular to the normal is there still a chance it may fall fully on the plane? and if so how would I show that it does not cross?