In R3\mathbb{R}^3R3, find the projection of vector v=(1,2,2)\mathbf{v} = (1, 2, 2)v=(1,2,2) onto the vector u=(1,0,0)\mathbf{u} = (1, 0, 0)u=(1,0,0).
(1,0,0)(1, 0, 0)(1,0,0)
13(1,2,2)\frac{1}{3}(1, 2, 2)31(1,2,2)
(0,2,2)(0, 2, 2)(0,2,2)
(1,2,2)(1, 2, 2)(1,2,2)