If the vectors a- and b- are mutually perpendicular- then a-a- a-a-b-

The correct option is C |#160; a|^4#160;b =a×(a×((a·b)a |a|^2b)) =(a×b×b( |a|^2)) =((a b)a |a|^2b)( |a|^2) =|a|^4b ...

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Byju's Answer

Standard XII

Mathematics

Combination of r Things from n Things When All Are Not Different

If the vector...

Question

If the vectors $\to a$ and $\to b$ are mutually perpendicular, then $\to a \times {\to a \times$ { $\to a \times (\to a \times \to b)}} =$

{| \to a |}^{2} \to b

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| \to b |^{4} \to a

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{| \to a |}^{4} \to b

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| \to a | \to b

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Solution

The correct option is C ${| \to a |}^{4} \to b$
$= ¯ ¯ ¯ a \times (¯ ¯ ¯ a \times ((¯ ¯ ¯ a \cdot ¯ ¯ b) ¯ ¯ ¯ a - | a |^{2} ¯ ¯ b))$
$= (¯ ¯ ¯ a \times ¯ ¯ b \times ¯ ¯ b (- | ¯ ¯ ¯ a |^{2}))$
$= ((¯ ¯ ¯ a - ¯ ¯ b) ¯ ¯ ¯ a - | a |^{2} ¯ ¯ b) (- | a |^{2})$
$= | a |^{4} ¯ ¯ b$

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If the vectors →a and →b are mutually perpendicular, then →a×{→a× {→a×(→a×→b)}}=

The correct option is C |→a|4→b=¯¯¯a×(¯¯¯a×((¯¯¯a⋅¯¯b)¯¯¯a−|a|2¯¯b))=(¯¯¯a×¯¯b×¯¯b(−|¯¯¯a|2))=((¯¯¯a−¯¯b)¯¯¯a−|a|2¯¯b)(−|a|2)=|a|4¯¯b

If the vectors $\to a$ and $\to b$ are mutually perpendicular, then $\to a \times {\to a \times$ { $\to a \times (\to a \times \to b)}} =$