If a-k- b-k- c-k- and a-k- then a-b-c-d- is a vector orthogonal to both

The correct option is B #160;k and #160;i a×b=2i 2k ...(i) c×d= 2i 2k ...(ii)Hence (2i 2k)×( 2i 2k) =4j+4j =8j Hence the re ...

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Multiplication of a Vector by a Scalar

If a⃗=î+ĵ+k...

Question

If $\to a =^i +^j +^k$ , $\to b =^i -^j +^k$ , $\to c =^i +^j -^k$ and $\to a =^i -^j -^k$ , then $(\to a \times \to b) \times (\to c \times \to d)$ is a vector orthogonal to both

^i

and

^j

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^j

and

^k

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^k

and

^i

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^i

and

^j

and

^j

and

^k

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

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

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

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

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

\to b =^i +^j -^k

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

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

| (\to a \times \to b) . (\to c \times \to d) | =

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

\to c = -^i +^j - 4^k

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

| (\to a \times \to b) \times (\to c \times \to d) |

\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 =

^i \times (^j \times^k) +^j \times (^k \times^i) +^k \times (^i \times^j) =

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