If a -b -c are three non coplanar- non zero vectors and r is any vector in space- then a -b -r -c -b -c -r -a -c -a -r -b is equal to - -a b c- Then the value of - is

Let T_1 = (a ×b )×(r ×c ) T_1 = [a b c]r [a b r]c Let T_2 = (b ×c )×(r ×a ) T_2 = [b c a]r [b c r]a =[a b c]r [b c r]a Let T_3 = (c ...

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Scalar Triple Product

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If $\to a, \to b, \to c$ are three non coplanar, non zero vectors and $\to r$ is any vector in space, then $(\to a \times \to b) \times (\to r \times \to c) + (\to b \times \to c) \times (\to r \times \to a) + (\to c \times \to a) \times (\to r \times \to b)$ is equal to $λ [\to a \to b \to c]$ . Then the value of $λ$ is

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\to a, \to b, \to c

\to r = \frac{(\to r . \to a) (\to b \times \to c) + (\to r . \to b) (\to c \times \to a) + (\to r . \to c) (\to a \times \to b)}{λ},

λ

\to a, \to b, \to c

\to r

\to r . \to a = 1, \to r . \to b = 2

\to r . \to c = 3.

[\to a, \to b, \to c] = 1

\to r

\to a, \to b, \to c

\to r . \to a = \to r . \to b = \to r . \to c = 0

\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 a, \to b, \to c

\to r

\to r . \to a = \to r . \to b = \to r . \to c = 1

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