Vector equation of a plane given 2 lines

[Skelly4444]

I am having trouble obtaining the vector equation of a plane that contains 2 known lines. The lines intersect at the point (1,-3,14).
The question asks for the Cartesian equation of the plane that contains these 2 lines and I'm not able to understand where I'm going wrong.

L1 (7,-3,2) + t(-1,0,2) and L2 (1,1,26) + s(0,1,3)

I follow the procedure to obtain 2 vectors from the 3 known points that lie in the plane, but when I do a vector product on these 2 vectors to obtain a normal vector, I get an answer that is nowhere near the correct one. The answer in the book is 2x -3y +z = 25

Any guidance would be appreciated as I'm completely baffled.

 

[blamocur]

I get an answer that is nowhere near the correct one.

Can you show us how you get your answer?
Thanks.

 

[Dr.Peterson]

I follow the procedure to obtain 2 vectors from the 3 known points that lie in the plane, but when I do a vector product on these 2 vectors to obtain a normal vector, I get an answer that is nowhere near the correct one.

But you are not given three points! (Well, you are, implicitly, but that's the long way.) You can get the two vectors directly from the equations of the lines. You are probably misinterpreting part of the problem.

We need to see your work (and your answer) in order to find your error.