Hi, can anyone show me how to prove this using an LP? Thanks!

Cones. Take a collection of m vectors in R, say V = {V1, V2, ..., Vm}. We say the vector z ER" is in the cone of V if and only if there exist non-negative numbers 11, 12, ..., Im such that z = 2 liVi. Prove that z is not in the cone of V if and only if there exists a vector w ER such that z is less than 90 degrees from w but every V; E V is at least 90 degrees from w