Question

Given vectors A, B and C such that A+B+C=0; ∣∣A∣∣ = 3, ∣∣B∣∣ = 1 and ∣∣C∣∣ = 4. calculate A dot B + B dot C + C dot A

Answer 1

since A+B = -C, and u•v = v•u,
A•B + B•C = (A+C)•B = -B•B = -1
B•C + C•A = (A+B)•C = -C•C = -4
A•B + B•C = (B+C)•A = -A•A = -3
add them all up and you have
2(A•B + B•C + C•A) = -8
A•B + B•C + C•A = -4