Finding Coplanar and Perpendicular Vectors with Given Length in 3D Vector Space

[linuxux]

Homework Statement

Given the vectors: V1=(3,1,2) and V2=(2,2,-1), find the set of vectors which are coplanar with V1 and V2 and also perpendicular to V3=(-2,1,1). Then Find the members of this set which have length 2-Root-11

Homework Equations

Dot and cross product

The Attempt at a Solution

well, a set of vectors coplanar to v1 and v2 would be V = (x,y,z) = (x',y',z') + rV1 +sV2
and a vector perpendicular to v3 in the set of vectors coplanar with v1 and v2 is: V X V3.
But what do i do with the 2-root-11?

 

[Dick]

VxV3 is not necessarily coplanar with V1 and V2. It's just perpendicular to whatever V you choose. Can you think of an expression using a dot product to express V perpendicular to V3? Finally the length of a vector is sqrt(v.v), right?

 

[linuxux]

okay, ill try it that way...