# The direction of a space vector is often given by its direction cosines. To describe these, let A = a i + b j + c k be a space vector, represented as an origin vector, and let α, β, and γ be the three angles (≤ π) that A makes respectively with i , j, and k . a) Show that dir A = cos α i + cos β j + cos γ k . (The three coefficients are called the direction cosines of A.) b) Express the direction cosines of A in terms of a, b, c; find the direction cosines of the vector − i + 2 j + 2 k . c) Prove that three numbers t, u, v are the direction cosine

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# The direction of a space vector is often given by its direction cosines. To describe these, let A = a i + b j + c k be a space vector, represented as an origin vector, and let α, β, and γ be the three angles (≤ π) that A makes respectively with i , j, and k . a) Show that dir A = cos α i + cos β j + cos γ k . (The three coefficients are called the direction cosines of A.) b) Express the direction cosines of A in terms of a, b, c; find the direction cosines of the vector − i + 2 j + 2 k . c) Prove that three numbers t, u, v are the direction cosine

OCW Scholar - Multivariable Calculus