If a-b-c are three non-coplanar vectors- p-q-r are non-zero vectors such that p- -b-c- a- b- c- - q- -c-a- a- b- c- - r- -a-b- a- b- c- then the value of the expression a- -b- -c- - p- -q- -r- is

The correct option is C 3 p = b × c #160;[ a b c #160;] #160; , q = c × a #160;[ a b c #160;] #160; , r = a × b ...

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Definition of a Determinant

If a,b,c ar...

Question

If $¯ ¯ ¯ a, ¯ ¯ b, ¯ ¯ c$ are three non-coplanar vectors, $¯ ¯ ¯ p, ¯ ¯ ¯ q, ¯ ¯ ¯ r$ are non-zero vectors such that $\to p = \frac{\to b \times \to c}{[\begin{matrix} \to a & \to b & \to c \end{matrix}]}, \to q = \frac{\to c \times \to a}{[\begin{matrix} \to a & \to b & \to c \end{matrix}]}, \to r = \frac{\to a \times \to b}{[\begin{matrix} \to a & \to b & \to c \end{matrix}]}$ , then the value of the expression $(\to a + \to b + \to c) . (\to p + \to q + \to r)$ is

0

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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

\to p, \to q, \to r

\to p = \frac{\to b \times \to c}{[\begin{matrix} \to b & \to c & \to a \end{matrix}]}

\to q = \frac{\to c \times \to a}{[\begin{matrix} \to c & \to a & \to b \end{matrix}]}

\to r = \frac{\to a \times \to b}{[\begin{matrix} \to a & \to b & \to c \end{matrix}]}

(\to a + \to b) . \to p + (\to b + \to c) . \to q + (\to c + \to a) . \to r

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 r

(\to a \times \to b) \times (\to r \times \to c) + (\to b \times \to c) \times (\to r \times \to a) + (\to c \times \to a) \times (\to r \times \to b) =

\to a, \to b, \to c

[\to a \to b \to c] \neq

{\to a}^{'}, {\to b}^{'}, {\to c}^{'}

\to r

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