Let a-b and c be three non-coplanar vectors- and let p-q and r be the vectors defined by the relation p-b- c-a b c- q-c- a-a b c- and r-a- b-a b c-Then the value of the expression a-b- p-b-c- q-c-a- r is equal to

The correct option is D 3 a· p=a· (b× c)/[a b c]=[a b c]/[a b c]=1 b· p=b· (b× c)/[a b c]=0/[a b c]=0 b· q=b· (c× a)/[a b c]=(b× c)· a/[a b ...

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Multinomial Theorem

Let a,b and...

Question

Let $a, b$ and $c$ be three non-coplanar vectors, and let $p, q$ and $r$ be the vectors defined by the relation
$p = \frac{b \times c}{[a b c]}, q = \frac{c \times a}{[a b c]},$ and $r = \frac{a \times b}{[a b c]},$
Then the value of the expression $(a + b) \cdot p + (b + c) \cdot q + (c + a) \cdot r$ is equal to

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Solution

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Similar questions

a, b

c

p, q

r

p = \frac{b \times c}{a b c}, q = \frac{c \times a}{a b c}

r = \frac{a \times b}{a b c}

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

\to a, \to b, \to c

\to p, \to q, \to r

\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]}

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

\to a, \to b, \to c

\to p, \to q, \to r

\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]},

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

\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]}

\to a, \to b

\to c

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

p = \frac{b \times c}{[a b c]}, q = \frac{c \times a}{[a b c]}, r = \frac{a \times b}{[a b c]}

a, b, c

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

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