Let i, j, and k be unit vectors along the positive x, y, and z axes of a rectangular coordinate system in 3-space. If v = (a, b, c) is a nonzero vector, then the angles α, β, and γ between v and the vectors i, j, and k, respectively, are called the direction angles of v (see accompanying figure), and the numbers cos α, cos β, and cos β are called the direction cosines of v.
Show that cos α= α / ||v||

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