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In a plane electromagnetic wave, the direction of electric field and magnetic field are represented by `hat"k"` and 2`hat"i" - 2hat"j"`, respectively. What is the unit vector along direction of propagation of the wave.

#### Options

`1/sqrt2(hat"i" + hat"j")`

`1/sqrt2(hat"j" + hat"k")`

`1/sqrt5(hat"i" + hat2"j")`

`1/sqrt5(hat2"i" + hat"j")`

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#### Solution

`bb(1/sqrt2(hat"i" + hat"j"))`

**Explanation:**

The direction of the electric and magnetic fields will not affect how an electromagnetic wave propagates.

`hat"C"=hat"E"xxhat"B"`

Here unit vector `hat"C"` is perpendicular to both `hat"E"` and `hat"B"`

Given, `vec"E"=hat"k", vec"B" = 2hat"i" - 2hat"j"`

∴ `hat"C"=hat"E"xxhat"B"`

= `1/sqrt2|(hat"i" hat"j" hat"k"), (0 0 1),(1 (-1) 0)|`

= `(hat"i"+hat"j")/sqrt2`

⇒ `hat"C" = (hat"i"+hat"j")/sqrt2`

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