If a- b- and c- are three non-coplanar vectors- then a-b-c- -a-b- -a-c- equalsA- 0B- -a-b-c-C- 2 -a-b-c-D- - ab c -

The correct option is D [ a⃗b⃗c⃗ ] ( a⃗+b⃗+c⃗). [ (a⃗+b⃗) × (a⃗+c⃗) ] =( a⃗+b⃗+c⃗). [ a⃗×a⃗ + a⃗×c⃗ + b⃗×a⃗ + b⃗×c⃗ ] ={a⃗.(a⃗×c⃗)+ a⃗.(b⃗×a⃗ ) + a⃗. (b⃗ ...

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Standard X

Mathematics

Scalar Triple Product

If a⃗, b⃗ and...

Question

If $\to a, \to b$ and $\to c$ are three non-coplanar vectors, then $(\to a + \to b + \to c) \cdot [(\to a + \to b) \times (\to a + \to c)]$ equals

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$[\to a \to b \to c]$

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$2. [\to a \to b \to c]$

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$- [\to a \to b \to c]$

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Solution

The correct option is D
$- [\to a \to b \to c]$

$(\to a + \to b + \to c) . [(\to a + \to b) \times (\to a + \to c)] = (\to a + \to b + \to c) . [\to a \times \to a + \to a \times \to c + \to b \times \to a + \to b \times \to c] = {\to a . (\to a \times \to c) + \to a . (\to b \times \to a) + \to a . (\to b \times \to c)} + {\to b . (\to a \times \to c) + \to b . (\to b \times \to a) + \to b . (\to b \times \to c)} + {\to c . (\to a \times \to c) + \to c . (\to b \times \to a) + \to c . (\to b \times \to c)} \Rightarrow [\to a \to b \to c] + [\to b \to a \to c] + [\to c \to b \to a] \Rightarrow - [\to a \to b \to c]$

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If →a,→b and →c are three non-coplanar vectors, then (→a+→b+→c)⋅[(→a+→b)×(→a+→c)] equals

If $\to a, \to b$ and $\to c$ are three non-coplanar vectors, then $(\to a + \to b + \to c) \cdot [(\to a + \to b) \times (\to a + \to c)]$ equals