vector space

**x-laplace** · May 5th 2010, 04:13 PM

hello friends

cone can help these problems

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

THANKS IN ADVANCE

**HallsofIvy** · May 6th 2010, 02:33 AM

Originally Posted by x-laplace

hello friends

cone can help these problems

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

I interpret this as meaning that the direct sum of the line and plane, as vector spaces is $R^3$ . One choice is the line perpendicular to the plane which has direction vector $2\vec{i}- \vec{j}+ 5\vec{k}$ .

2) $L=r(1,-1,1) / r \in R$ .
Find 2 straight $L_1$ y $L_2$ in $R^3$ such that $L+L_1+L_2=R^3$

Again, there are an infinite number of answers. The simplest thing to do is to choose lines orthogonal to L: $L_1= s(1, 1, 0)$ and [maht]L_2= t(0, 1, 1) will work.

THANKS IN ADVANCE

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