The correct option is B 2(#160;a×#160;b) =(a×b) ((a×b)·i)i+(a×b) ((a×b)·j)j+(a×b) ((a×b)·k)k =3(a×b) ((a×b)·i)i ((a×b)·j)j ((a×b)·k)k =2(a× ...

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Applications of Cross Product

î×[a⃗×b⃗×î]+j...

Question

$^i \times [(\to a \times \to b) \times^i] + ¯ j \times [(\to a \times \to b) \times^j] + ¯ ¯ ¯ k \times [(\to a \times \to b) \times^k]$

\to 0

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(\to a \cdot \to b) \to b

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\to b

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2 (\to a \times \to b)

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Solution

The correct option is B $2 (\to a \times \to b)$
$= (¯ ¯ ¯ a \times ¯ ¯ b) - ((¯ ¯ ¯ a \times ¯ ¯ b) \cdot ¯ i) ¯ i + (¯ ¯ ¯ a \times ¯ ¯ b) - ((¯ ¯ ¯ a \times ¯ ¯ b) \cdot ¯ j) ¯ j + (¯ ¯ ¯ a \times ¯ ¯ b) - ((¯ ¯ ¯ a \times ¯ ¯ b) \cdot ¯ ¯ ¯ k) ¯ ¯ ¯ k$
$= 3 (¯ ¯ ¯ a \times ¯ ¯ b) - ((¯ ¯ ¯ a \times ¯ ¯ b) \cdot ¯ i) ¯ i - ((¯ ¯ ¯ a \times ¯ ¯ b) \cdot ¯ j) ¯ j - ((¯ ¯ ¯ a \times ¯ ¯ b) \cdot ¯ ¯ ¯ k) ¯ ¯ ¯ k$
$= 2 (¯ ¯ ¯ a \times ¯ ¯ b)$

Suggest Corrections

Similar questions

\to a =^i +^j, \to b =^i +^k

{{(\to a \times \to b) \times \to a} \times \to a} \times \to b =

\to a =^i +^j +^k

\to b = - 3^i +^k

\to c =^i + 2^j + 3^k

A)

[\to a \times \to b

\to b \times \to c

\to c \times \to a]

B)

[\to a + \to b

\to b + \to c

\to c + \to a]

C)

[\to a

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\to c]

[\to a

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\to c]^{- 1}

D)

[\to a - \to b

\to b - \to c

\to c - \to a]

\to a =^j -^k

\to c =^i -^j -^k

\to b

\to a \times \to b + \to c = \to 0

\to a \cdot \to b = 3

\to a =^i +^j + 2^k

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(\to a + 3 \to b) . (2 \to a - \to b)

\to a =^i +^j +^k, \to b =^i -^j +^k, \to c =^2 i +^3 j -^k

(\to a \times \to b) \times \to c =

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