The correct option is B (a.b)|a×b|^2 (a×(b×a)).(b×(a×b)) =|a.b amp;a.a×b nbsp; nbsp;b×a.b amp;(b×a).(a×b)| by scalar four produc ...

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Magnetic Flux and Magnetic Flux Density

a×b×a.b×a×b=

Question

$(\to a \times \to b \times \to a) . (\to b \times \to a \times \to b) =$

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

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- (\to a . \to b) {∣ ∣ ∣ \to a \times \to b ∣ ∣ ∣}^{2}

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{∣ ∣ \to a ∣ ∣}^{2} {∣ ∣ ∣ \to a \times \to b ∣ ∣ ∣}^{2}

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{∣ ∣ ∣ \to b ∣ ∣ ∣}^{2} {∣ ∣ ∣ \to a \times \to b ∣ ∣ ∣}^{2}

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Solution

The correct option is B $- (\to a . \to b) {∣ ∣ ∣ \to a \times \to b ∣ ∣ ∣}^{2}$
$(\to a \times (\to b \times \to a)) . (\to b \times (\to a \times \to b))$
$= ∣ ∣ ∣ ∣ ∣ \begin{matrix} \to a . \to b & \to a . \to a \times \to b \to b \times \to a . \to b & (\to b \times \to a) . (\to a \times \to b) \end{matrix} ∣ ∣ ∣ ∣ ∣$ by scalar four product
$= - (\to a . \to b) {∣ ∣ ∣ \to a \times \to b ∣ ∣ ∣}^{2} - 0$ since vector product of same vectors $= 0$
$= - (\to a . \to b) {∣ ∣ ∣ \to a \times \to b ∣ ∣ ∣}^{2}$

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Similar questions

I

| ¯ ¯ ¯ a . ¯ ¯ b | = | ¯ ¯ ¯ a \times ¯ ¯ b |

(¯ ¯ ¯ a . ¯ ¯ b) = \frac{π}{4}

II

| ¯ ¯ ¯ a . ¯ ¯ b |^{2} = | ¯ ¯ ¯ a \times ¯ ¯ b |^{2}

(¯ ¯ ¯ a, ¯ ¯ b) = \frac{3 π}{4}

| a \times b |^{2} = (a . a) (b .) - (a . b)^{2} = a^{2} b^{2} - (a . b)^{2}

| ¯ ¯ ¯ a . ¯ ¯ b |^{2} + | ¯ ¯ ¯ a \times ¯ ¯ b |^{2}

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

p =

| a \times b | = 4 a n d | a . b | = 2, t h e n {| a |}^{2} {| b |}^{2}

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