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Let 1, 2, and 3 be three perpendicular unit vectors, whose , , k components are unknown. a. Let a = 1+22+33. Compute the dot products a , 2, and , using the rules (A1)-(A3). b. Let 6=41 +52 +63. Evaluate the dot product a 5, using the rules (A1)-(A3). . c. Let = v+v + vk and w = w+w+wk. Verify the algebraic formula for the dot product, vw vw1+V2W2 + V3W3, using the rules (A1)-(A3). = = (A1) for any vectors and w. (A2) (A3) . . (12) = wi+w2 for any vectors , w, and w2. (ku)=k() for any vectors and wand any scalar k.