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Question Number 6374 by sanusihammed last updated on 25/Jun/16

S h o w t h a t

\bar{a} \times (b \times c) = (\bar{a} . \bar{c}) \bar{b} - (\bar{a} . \bar{b}) \bar{c}

Commented by FilupSmith last updated on 25/Jun/16

what is the difference between

a and \bar{a} ?

Commented by prakash jain last updated on 25/Jun/16

I think he meant vector :

\vec{a} \times (\vec{b} \times \vec{c}) = (\vec{a} \cdot \vec{c}) \vec{b} - (\vec{a} \cdot \vec{b}) \vec{c}

a \times (b \times c) = (a \cdot c) b - (a \cdot b) c

Commented by FilupSmith last updated on 25/Jun/16

note :

t =< t_{1}, t_{2}, \dots, t_{g} >= [\begin{matrix} t_{1} \\ t_{2} \\ ⋮ \\ t_{g} \end{matrix}], t \in R^{g}

I will be using this notation for simplicity .

a =< a_{1}, \dots, a_{n} >

b =< b_{1}, \dots, b_{n} >

c =< c_{1}, \dots, c_{n} >

a, b, c \in R^{n}

a \times b =∥ a ∥∥ b ∥ \sin (θ) n \to vector

a ∙ b =∥ a ∥∥ b ∥ \cos (θ) \to scalar

∥ t ∥= \sqrt{t_{1}^{2} + t_{2}^{2} + \dots + t_{n}^{2}} \to scalar

where n is the unit vector perpendicular

to a and b .

Question :

a \times (b \times c) = (a ∙ c) b - (a ∙ b) c

because a ∙ b and a ∙ c are scalars,

multiplying them by a vector makes

a new vector .

e . g . 5 ⟨ 2, 1 ⟩ = ⟨ 10, 5 ⟩

continue