Determining Coordinates - lines and planes

[ttpp1124]

Homework Statement

Use normal vectors to determine the intersection, if any, for each of the following groups of three planes. Give a geometric interpretation in each case and the number of solutions for the corresponding linear system of equations. If the planes intersect in a line, determine a vector equation of the line. If the planes intersect in a point, determine the coordinates of the point.

I solved it, I just need someone to check my work. Thanks in advance!

Relevant Equations

n/a

 

[FactChecker]

You should plug the answers you got into the original equations and see if they satisfy all the equations.

 

[ttpp1124]

You should plug the answers you got into the original equations and see if they satisfy all the equations.

Just did, and I got my desired outcome. Thanks!

 

[FactChecker]

To conclude that the solution set is a single point, you should notice that there was enough information to get one specific value for each variable. If there are more than one point in the solution set, your final answer will have one (or more) variable in terms of the others and you will not be able to go further.