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## Homework Statement

I require some help to find a non-zero vector in R^3 that belongs both to span {y; u} and to span {v;w} where y = (1; 0; 0); u = (0; 0; 1), v = (1; 1; 1) and w = (2; 3;-1),

I need to know if my below solutions is ok.Thank you

**2. The attempt at a solution**Let 'a' be the required vector.

I need to satisfy [a,y,u]=0 and [a,v,w]=0; where [a,y,u] is the scalar triple product of a, y and u.

Since span of two given vectors is a plane, 'a' lies on the intersection of two planes hence 'a' is the vector along the line of intersection of the two planes.

=>.....[A,B,C]=det(ABC)...so det(a,y,u)=>y=0....and det(a,v,w)=-4x+y+z=0.....y=0,so x=1 and z=4