1)Use Lagrange multipliers to find shortest distance from (10,-4,9) to the plane 7x+8y-10z=4
- I tried to use d=sqrt((x-10)^2+(y+4)^2+(z-9)^2) then split each one up to 2(x-10)=7h , 2(y+4)=8h , 2(z-9)=-10h
- I then solved for x,y,z and plugged into the original equation of 7x+8y-10z=4 got I got h=112/213 which is not correct and I'm not sure where I messed up.
2)Use lagrange multipliers to find volume of largest rectangular box in first octant with 3 faces in coordinate planes and one vertex in plane x+5y+2z=30.
-I use V=xyz and got yz=h , xz=5h , xy=2h , x+5y+2z=30
- Not sure where to go after this.