If p-q-r is reciprocal system of vector triad a-b and c- then -abc-pqr-

Name: JEE- Grade 12- Mathematics- Vector Algebra- Session 09- W16
Uploaded: 2022-07-04T10:36:42+05:30
Description: As p,q,r is reciprocal system of vector triad a,b and c nbsp; ⇒ nbsp;[abc]=1[pqr] ⇒ [abc][pqr]=1 ...

As p,q,r is reciprocal system of vector triad a,b and c nbsp; ⇒ nbsp;[abc]=1[pqr] ⇒ [abc][pqr]=1 ...

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Standard XII

Mathematics

Equation of a Plane : Vector Form

If p,q,r is r...

Question

If $\to p, \to q, \to r$ is reciprocal system of vector triad $\to a, \to b$ and $\to c,$ then $[\to a \to b \to c] [\to p \to q \to r] =$

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Solution

As $\to p, \to q, \to r$ is reciprocal system of vector triad $\to a, \to b$ and $\to c$
$\Rightarrow [\to a \to b \to c] = \frac{1}{[\to p \to q \to r]}$
$\Rightarrow [\to a \to b \to c] [\to p \to q \to r] = 1$

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Similar questions

Q. If

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and

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and

\to r

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and

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, then the value of

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\to a, \to b, \to c

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\to a . \to p + \to b . \to q + \to c . \to r = 3

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\to q

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Q. If

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are three non-coplanar vectors, and

\to p, \to q, \to r

are reciprocal vectors to

\to a, \to b, \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

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\to p, \to p, \to r

as defined as

\to p = \frac{\to b \times \to c}{[\to b \to c \to a]}, \to q = \frac{\to c \times \to a}{[\to c \to a \to b]}, \to r = \frac{\to a \times \to b}{[\to a \to b \to c]}, (\to a + \to b) . \to p + (\to b + \to c) . \to q + (\to c + \to a) . \to r

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are sets of three non-coplanar unit vectors such that

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Equation of a Plane : Vector Form

Standard XII Mathematics

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If →p,→q,→r is reciprocal system of vector triad →a,→b and →c, then [→a→b→c][→p→q→r]=

As →p,→q,→r is reciprocal system of vector triad →a,→b and →c ⇒[→a→b→c]=1[→p→q→r] ⇒[→a→b→c][→p→q→r]=1

If $\to p, \to q, \to r$ is reciprocal system of vector triad $\to a, \to b$ and $\to c,$ then $[\to a \to b \to c] [\to p \to q \to r] =$

As $\to p, \to q, \to r$ is reciprocal system of vector triad $\to a, \to b$ and $\to c$
$\Rightarrow [\to a \to b \to c] = \frac{1}{[\to p \to q \to r]}$
$\Rightarrow [\to a \to b \to c] [\to p \to q \to r] = 1$