Determine the projection of vector a onto vector b. Next, express vector a as vectors, a₁ and a₂, where a₁ is parallel to vector b and a₂ is perpendicular to vector b. 
a = 12i +5j, b = 2i +6j

• A. proj_b(a) = (27/10)i + (81/10)j , a₁ = (27/10)i + (81/10)j ; a₂ = (93/10)i -(31/10)j
• B. proj_b(a) = 27i + 81j, a₁ = 27i + 81j; a₂ = (93/10)i -(31/10)j
• C. proj_b(a) = (27/10)i + (27/5)j, a₁ = (27/10)i + (27/5)j; a₂ = 93i -4j
• D. proj_b(a) = (27/10)i - (27/5)j, a₁ = (27/10)i - (27/5)j; a₂ = (93/10)i +(4/10)j

Answer: (A)