Mathematica needed to solve question You should make use of Mathematica as appro
ID: 2836417 • Letter: M
Question
Mathematica needed to solve question
You should make use of Mathematica as appropriate to avoid having to find dot
products, cross products, etc. by hand. Your explanations should be written as text
regions in Mathematica.
Find the plane that passes through the point (-1,1,1) and which contains the line of intersection between the planes: x+y-z=1 and 4x-y+5z=3. Your explanation of your thought process must be very clear.
Remember Mathematica must be used to get these solutions.
Explanation / Answer
Almost any plane thro intersection of given planes is (x+y-z-1) + Lembda(4x-y+5z-3) = 0
This is because the equation is linear in x,y,z (and so it is a plane) and any points that satisfy both x+y-z-1=0 and 4x-y+5z-3=0 obviously satisfy this equation as well, so it contains the intersection.
Inserting (-1,1,1) gives (-2) + lamda(-11) = 0 lambda = -2/11
The required plane is (x+y-z-1)