If a- -b- -c- are non coplanar and - a-b-c- - 4 7- then - 2a- -b- -2b- -c- -2c- -a- is

[ 2a⃗ b⃗ , 2b⃗ c⃗ , 2c⃗ a⃗ #160; ] =( 2a⃗ b⃗ #160; ) [ ( 2b⃗ c⃗ #160; ) ·( 2c⃗ a⃗ #160; ) #160; ] =( 2a⃗ b⃗ #160; ) [ 4b⃗ .c⃗ ...

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Condition for Coplanarity of Four Points

If a⃗ ,b⃗ ,...

Question

If $\to a, \to b, \to c$ are non coplanar and $[\to a \to b \to c] = \frac{4}{7}$ , then $[2 \to a - \to b, 2 \to b - \to c, 2 \to c - \to a]$ is

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\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

\frac{[\begin{matrix} \to a + 2 \to b & \to b + 2 \to c & \to c + 2 \to a \end{matrix}]}{[\begin{matrix} \to a & \to b & \to c \end{matrix}]}

\to a, \to b, \to c

2 \to a + \to b, \to a + 2 \to b + \to c, 4 \to a - 2 \to b - \to c

3 \to a + 4 \to b - 5 \to c

\to a, \to b, \to c

_{1} = \to a - \to b + \to c,_{2} = \to b + \to c - \to a

_{3} = \to c + \to a - \to b, \to r = 2 \to a - 2 \to b + 4 \to c

\to r = x_{1}_{1} + x_{2}_{2} + x_{3}_{3}

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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