If b and c are mutually perpendicular unit vectors and a is any vector- then a -bb - a -cc - a - b-c- b-c- b-c -

#10; #10;Given that #10; #10; ( #10;a.b)b+( #10;a.c)c+a(b× #10;c)| b×c #10;|(b×c) #10; #10;And b #10;c #160;hence, b× ...

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If b and ...

Question

If $\to b$ and $\to c$ are mutually perpendicular unit vectors and $\to a$ is any vector, then $(\to a, \to b) \to b + (\to a . \to c) \to c + \frac{\to a . (\to b \times \to c)}{∣ ∣ ∣ \to b \times \to c ∣ ∣ ∣} (\to b \times \to c) =$

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\to b

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(\to a . \to b) \to b + (\to a . \to c) \to c + \frac{\to a (\to b \times \to c)}{{∣ ∣ ∣ \to b \times \to c ∣ ∣ ∣}^{2}} (\to b \times \to c)

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(a . b) b + (a . c) + \frac{a . b \times c}{| b \times c |} . (b \times c)

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(a \cdot b) b + (a \cdot c) c + \frac{a \cdot (b \times c)}{{| b \times c |}^{2}} (b \times c)

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(a . b) b + (a . c) c + \frac{a . (b + c)}{{| b + c |}^{2}} (b \times c) =

a \times (b \times c), b \times (c \times a)

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