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Dot Product of Two Vectors

If b×c×c×a=3c...

Question

If $(\to b \times \to c) \times (\to c \times \to a) = 3 \to c,$ then $[\to b \times \to c \to c \times \to a \to a \times \to b]$ is equal to

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Solution

Given : $(\to b \times \to c) \times (\to c \times \to a) = 3 \to c$
$\Rightarrow [\to b \to c \to a] \to c - [\to b \to c \to c] \to a = 3 \to c \Rightarrow [\to b \to c \to a] \to c - \to 0 = 3 \to c \Rightarrow [\to b \to c \to a] = 3 \dots (i)$
Now,
$[\to b \times \to c \to c \times \to a \to a \times \to b] = (\to a \times \to b) \cdot {(\to b \times \to c) \times (\to c \times \to a)} = (\to a \times \to b) \cdot 3 \to c = 3 [\to a \to b \to c] = 9$
(from $(i)$ )

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Dot Product of Two Vectors

Standard XII Mathematics

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