If a-2-4k-b-2-3-k- c-4-4k- then the vector a-b-c- is orthogonal to

The correct option is D a⃗ a⃗× (b⃗×c⃗)= (a⃗·c⃗)b⃗ (a⃗·b⃗)c⃗ = 7b⃗ 0 a⃗× (b⃗×c⃗)= 7b⃗ a⃗·b⃗= 0 a⃗· (a⃗× (b⃗×c⃗))= 7a⃗·b⃗ ...

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Byju's Answer

Standard XII

Mathematics

Multiplication of a Vector by a Scalar

If a⃗=î+2ĵ+...

Question

If $\to a =^i + 2^j + 4^k, \to b = 2^i - 3^j +^k$ , $\to c =^i + 4^j - 4^k$ then the vector $\to a \times (\to b \times \to c)$ is orthogonal to

\to a

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\to b

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\to c

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\to a + \to b + \to c

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Solution

The correct option is D $\to a$
$\to a \times (\to b \times \to c) = (\to a \cdot \to c) \to b - (\to a \cdot \to b) \to c$
$= - 7 \to b - 0$
$\to a \times (\to b \times \to c) = - 7 \to b$
$\to a \cdot \to b = 0$
$\to a \cdot (\to a \times (\to b \times \to c)) = - 7 \to a \cdot \to b$
$= 0$

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If →a=^i+2^j+4^k,→b=2^i−3^j+^k,→c=^i+4^j−4^k then the vector →a×(→b×→c) is orthogonal to

The correct option is D →a→a×(→b×→c)=(→a⋅→c)→b − (→a⋅→b)→c=−7→b−0→a×(→b×→c)=−7→b→a⋅→b=0→a⋅(→a×(→b×→c))=−7→a⋅→b=0

If $\to a =^i + 2^j + 4^k, \to b = 2^i - 3^j +^k$ , $\to c =^i + 4^j - 4^k$ then the vector $\to a \times (\to b \times \to c)$ is orthogonal to

The correct option is D $\to a$
$\to a \times (\to b \times \to c) = (\to a \cdot \to c) \to b - (\to a \cdot \to b) \to c$
$= - 7 \to b - 0$
$\to a \times (\to b \times \to c) = - 7 \to b$
$\to a \cdot \to b = 0$
$\to a \cdot (\to a \times (\to b \times \to c)) = - 7 \to a \cdot \to b$
$= 0$