Question

If are unit vectors such that , find the value of .

Answer 1

The given vectors a → , b → and c → are unit vectors and a → + b → + c → =0.

Now,

| a → + b → + c → | 2 =0 ( a → + b → + c → )⋅( a → + b → + c → )=0 | a → | 2 + | b → | 2 + | c → | 2 +2( a → ⋅ b → + b → ⋅ c → + c → ⋅ a → )=0

Substitute the values of | a → |, | b → | and | c → | in the above equation.

1 2 + 1 2 + 1 2 +2( a → ⋅ b → + b → ⋅ c → + c → ⋅ a → )=0 3+2( a → ⋅ b → + b → ⋅ c → + c → ⋅ a → )=0 ( a → ⋅ b → + b → ⋅ c → + c → ⋅ a → )= −3 2

Thus, the value of ( a → ⋅ b → + b → ⋅ c → + c → ⋅ a → ) is −3 2 .