If p-b-c-abc- q-c-a-abc- and r-a-b-abc- where a- b and c are three non-coplanar vectors- then the value of the expression a-b-c-p-q-r is

A·p=a·(b× nbsp;c)[abc] =a·(b× nbsp;c)[abc] =[abc][abc]=1 a·q=a·(c× nbsp;a)[abc] =a·(c× nbsp;a)[abc] =[aca][abc]=0 nbsp; Sim ...

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Scalar Triple Product

If p=b×c[abc]...

Question

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

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\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)

\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 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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