If a-b-c- are three non- coplanar vectors for which - a-b-c- - a-b-c- constitute the reciprocal system of vectors- then any vector r- can be expressed as

The correct option is C r⃗= ( r⃗. a⃗' )a⃗+ ( r⃗. b⃗' )b⃗+ ( r⃗. c⃗' )c⃗ Let r be expressed as a linear combination of the non coplanarvector ...

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Definition of Function

If a⃗,b⃗,c⃗...

Question

If $\to a, \to b, \to c$ are three non- coplanar vectors for which $[\to a \to b \to c] \neq$ ${\to a}^{'}, {\to b}^{'}, {\to c}^{'}$ constitute the reciprocal system of vectors, then any vector $\to r$ can be expressed as

\to r = (\to r \times \to a) . {\to a}^{'} + (\to r \times \to b) . {\to b}^{'} + (\to r \times \to c) . {\to c}^{'}

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\to r = (\to r \times {\to a}^{'}) . \to a + (\to r \times {\to b}^{'}) . \to b + (\to r \times {\to c}^{'}) . \to c

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\to r = (\to r . \to a) . {\to a}^{'} + (\to r . \to b) . {\to b}^{'} + (\to r . \to c) . {\to c}^{'}

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\to r = (\to r . {\to a}^{'}) \to a + (\to r . {\to b}^{'}) \to b + (\to r . {\to c}^{'}) \to c

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