Question

A, B, C are 3 unit vectors. Show
(A-B)^2+(B-C)^2+(C-A)^2<=9​

Answer 1

Answer:

Step-by-step explanation:

∣a−b∣  2  +∣b−c∣  2+∣c−a∣  2 =2(a  2  +b  2 +c  2  )−2(a.b+b.c+c.a) =2×3−2(a.b+b.c+c.a) =6−{(a+b+c)  2  −a  2  −b  2 −c  2  } =9−∣a+b+c∣  2≤9

Hence, option B.