1. vector space

hello friends

cone can help these problems

1)Given $\displaystyle V=(x,y,z)\in{R}^3/2x-y+5z=0$. Find a line L $\displaystyle / V+L=R^3$
2)$\displaystyle L=r(1,-1,1) / r \in R$.
Find 2 straight $\displaystyle L_1$ y $\displaystyle L_2$ in $\displaystyle R^3$ such that $\displaystyle L+L_1+L_2=R^3$

2. Originally Posted by x-laplace
hello friends

cone can help these problems

1)Given $\displaystyle V=(x,y,z)\in{R}^3/2x-y+5z=0$. Find a line L $\displaystyle / V+L=R^3$
I interpret this as meaning that the direct sum of the line and plane, as vector spaces is $\displaystyle R^3$. One choice is the line perpendicular to the plane which has direction vector $\displaystyle 2\vec{i}- \vec{j}+ 5\vec{k}$.

2)$\displaystyle L=r(1,-1,1) / r \in R$.
Find 2 straight $\displaystyle L_1$ y $\displaystyle L_2$ in $\displaystyle R^3$ such that $\displaystyle L+L_1+L_2=R^3$
Again, there are an infinite number of answers. The simplest thing to do is to choose lines orthogonal to L: $\displaystyle L_1= s(1, 1, 0)$ and [maht]L_2= t(0, 1, 1) will work.