If a- b and c are three non-coplanar vectors and p- q and r are vectors defined by p-b-c-abc- q-c-a-abc- and r-a-b-abc- then the value of a-b-p-b-c-q-c-a-r -

The correct option is D 3Given that: p⃗ = b⃗×c⃗[a⃗b⃗c⃗] . #160; q⃗ = c⃗×a⃗[a⃗b⃗c⃗] , #160; r⃗ = a⃗×b⃗[a⃗b⃗c⃗] =(a⃗ + b⃗).p⃗ + (b⃗ + c⃗).q ...

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Test for Collinearity of Points

If a, b and...

Question

If $\to a, \to b$ and $\to c$ are three non-coplanar vectors and $\to p, \to q$ and $\to r$ are vectors defined by $\to p = \frac{\to b \times \to c}{[\to a \to b \to c]}, \to q = \frac{\to c \times \to a}{[\to a \to b \to c]}$ and $\to r = \frac{\to a \times \to b}{[\to a \to b \to c]}$ , then the value of
$(\to a + \to b) \cdot \to p + (\to b + \to c) \cdot \to q + (\to c + \to a) \cdot \to r =$

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\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)

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 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)

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

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