If a-k- and b-k- then find a vector c- such that a-c-b- and a-c-3 - -

Let c=xî+yĵ+zk̂ Also, a=î+ĵ+k̂ and b̂=ĵ k̂ For a×c=b, î amp; ĵ amp;k̂ 1 amp; 1 amp;1 x amp; y amp;z =ĵ k̂ ⇒ î(z y) ĵ(z x)+k̂(y x ...

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Applications of Cross Product

If a⃗=î-ĵ+k̂ ...

Question

If $\to a =^i -^j +^k a n d \to b =^j -^k,$ then find a vector $\to c$ such that $\to a \times \to c = \to b a n d \to a . \to c = 3.....$

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

\to b =^j -^k,

\to c

\to a . \to c = 3

\to a \times \to c = \to b

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

\to b

\to a \times \to b = \to c

\to a \cdot \to b = 3.

| \to b |

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

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

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

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

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

\to c

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

\to a \cdot \to c = 4

| \to c |^{2}

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