Use orthogonal projections to find the distance from the point (2, 3, 4) to the plane 2x + y + z = 0.
Show that if uᵢ, dots, uₖ are pairwise orthogonal vectors such that ||uᵢ|| = 1 for all i, then ||c₁u₁ + c dots + cₖuₖ||² = c₁² + c dots + cₖ²
a). Let x = [1] [-2] [3] and y = [-1] [1] [4]. Find these four matrix products: xᵀᵀy, yxᵀᵀ, yᵀᵀxy, and yyᵀᵀx.