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If vec a and vec b are two vectors, the...

If ` vec a` and `vec b` are two vectors, then prove that `( vec axx vec b)^2=|[vec a.vec a,vec a.vec b],[vec b.vec a,vec b.vec b]|` .

Text Solution

Verified by Experts

`(vecaxxvecb)^(2)=(ab sintheta.hatn)^(2)`
`=a^(2)b^(2)sin^(2)theta`
=`(veca.veca) (vecb.vecb)-(veca.vecb)^(2)`
`=|{:(veca.veca" ",veca.vecb),(vecb.veca" ",vecb.vecb):}|`
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