If A- B- and C- are three non-coplanar vectors then A-B-C- -A-B- A-C- equals-

The correct option is C [A⃗B⃗C⃗] (A⃗+B⃗+C⃗).((A⃗+B⃗)× (A⃗+C⃗)) =(A⃗+B⃗+C⃗).(B⃗×A⃗+A⃗×C⃗+B⃗×C⃗) =(A⃗+B⃗+C⃗).(B⃗×A⃗)+(A⃗+B⃗+C⃗).(A⃗×C⃗)+(A⃗+ ...

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Test for Coplanarity

If A⃗, B⃗ a...

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?

0

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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

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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

\to a, \to b, \to c

\to p = \frac{\to b \times \to c}{[\to a \to b \to c]}

\to q = \frac{\to c \times \to a}{[\to a \to b \to c]}

\to r = \frac{\to a \times \to b}{[\to a \to b \to c]}

(2 \to a + 3 \to b + 4 \to c) . \to p + (2 \to b + 3 \to c + 4 \to a) . \to q +

(2 \to c + 3 \to a + 4 \to b) . \to r =

\to A, \to B

\to C

(\to A + \to B + \to C) . [(\to A + \to B) \times (\to A + \to C)]

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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