# Why is there unique plane which passes through given point and is parallel to given line

I was trying to solve one question which is asking to find a plane which passes through given point and is parallel to given line.

The given point is $$M(2,-5,3)$$ and the given line is given as an interesection of the planes $$2x-y+3z-1=0 \text{ and } 5x+4y-z-7=0$$

It is still unclear for me why there is only one unique plane which can be answer, I think that there are more possible planes that can be answers to this.

• Perhaps you might include the specific problem that you’re asking about. – amd Mar 13 at 19:40
• I inserted the given point and the line into the post – someone123123 Mar 13 at 20:30
• Are you sure that the problem said for the plane to be parallel to that line? If it must instead include the line, then the solution is be unique. – amd Mar 13 at 20:35
• Yes, the question is asking about plane which is parallel to the given line. – someone123123 Mar 13 at 20:45

Your are right, such plane is not unique. For example the planes $$2x-y+3z=18$$ and $$5x+4y-z=-13$$ pass through the point $$(2,-5,3)$$ and they are parallel to the given line.