If , are unit vectors and then the value of of is :

Question

Question

Answer 1

Concept:

Dot Product: it is also called the inner product or scalar product

Let the two vectors are and

Dot Product of two vectors is given by: = |a||b| cos θ

Where || = Magnitudes of vectors a, || = Magnitudes of vectors b and θ is the angle between a and b

Formulas of Dot Product:

Calculation:

Given that,

(â + b̂ + ĉ) = 0 ----(1)

We know that,

(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca

⇒ (â + b̂ + ĉ)² = â ⋅ â + b̂ ⋅ b̂ + ĉ ⋅ ĉ + 2(â ⋅ b̂ + b̂ ⋅ ĉ + ĉ ⋅ â)

From equation (1), we get

⇒ (1 + 1 + 1) + 2 (â ⋅ b̂ + b̂ ⋅ ĉ + ĉ ⋅ â) = 0

∴ (â ⋅ b̂ + b̂ ⋅ ĉ + ĉ ⋅ â) = - 3/2

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