If a-b-c- are three non-coplanar and p-q-r- are reciprocal vectors to a-b- and c- respectively then la-mb-nc- - lp-mq-nr- is equal to - where l- m- n are scalars

The correct option is A l^2+m^2+n^2 Given a⃗,b⃗,c⃗ are three non coplanar and p⃗,q⃗,r⃗ are reciprocal vectors to a⃗,b⃗ and c⃗ resp ...

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Sum of Coefficients of All Terms

If a⃗,b⃗,c⃗...

Question

If $\to a, \to b, \to c$ are three non-coplanar and $\to p, \to q, \to r$ are reciprocal vectors to $\to a, \to b$ and $\to c$ respectively then $(l \to a + m \to b + n \to c) . (l \to p + m \to q + n \to r)$ is equal to : (where l, m, n are scalars)

l^{2} + m^{2} + n^{2}

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l m + m n + n l

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none of these

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\to a, \to b, \to c

\to p, \to q, \to r

(\to a \times \to p) + (\to b \times \to q) + (\to c \times \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

\to a \times (\to b \times \to c), \to b \times (\to c \times \to a), \to c \times (\to a \times \to b)

l, m, n

l \to a + m \to b + n \to c = \to 0

\to a, \to b, \to c

The scalars l and m such that $l \to a + m \to b = \to c$ where $\to a, \to b$ and $\to c$ are given vectors, are equal to

¯ ¯ ¯ a, ¯ ¯ b, ¯ ¯ c

¯ ¯ ¯ p, ¯ ¯ ¯ q, ¯ ¯ ¯ r

\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}]}

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

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