Equation for a plane containing two lines a point

[mconway]

The question is Find equation of a plane containing the lines x-y+2z = 4, 2x + y + 3z = 6, and the point (1,-2,4).

The answer to the question is 8x + 13y + 9z - 18 =0, I have no idea how to get that.

I thought that you could find the cross product using (1,-1,2) x (2,1,3), but that gives you -5i + j + 3k or (-5,1,3), then use that to find the equation of the plane, using the points.

Can someone explain how to get the answer? Thanks.

 

[Ishuda]

The question is Find equation of a plane containing the lines x-y+2z = 4, 2x + y + 3z = 6, and the point (1,-2,4).

The answer to the question is 8x + 13y + 9z - 18 =0, I have no idea how to get that.

I thought that you could find the cross product using (1,-1,2) x (2,1,3), but that gives you -5i + j + 3k or (-5,1,3), then use that to find the equation of the plane, using the points.

Can someone explain how to get the answer? Thanks.

Something is wrong with the problem as worded. First of all, the two equations you have describe different planes, not lines. Secondly, in general, a plane can not contain two lines unless the lines meet special conditions. Just as a line is determined by two different points, a plane is determined by three non co-linear points.

 

[mconway]

Something is wrong with the problem as worded. First of all, the two equations you have describe different planes, not lines. Secondly, in general, a plane can not contain two lines unless the lines meet special conditions. Just as a line is determined by two different points, a plane is determined by three non co-linear points.

I was a bit confused as well, but that's what the question says.

It's question 7 below. The answer is supposed to be 8x + 13y + 9z - 18 =0. I have no idea how to get that.