Let \(\vec {a} = 3{\rm{\hat i}} + 2{\rm{\hat j}} + 2{\rm{\hat k\;and\;\vec b}} = {\rm{\hat i}} + 2{\rm{\hat j}} - 2{\rm{\hat k}}\) be two vectors. If a vector perpendicular to both the vectors \(\overrightarrow {a} + {\rm{\vec b\;and\;}}\overrightarrow {a} - {\rm{\vec b}}\) has the magnitude 12 then one such vector is:
1
\(4\left( {2{\rm{\hat i}} + 2{\rm{\hat j}} + {\rm{\hat k}}} \right)\)
2
\(4\left( {2{\rm{\hat i}} - 2{\rm{\hat j}} - {\rm{\hat k}}} \right)\)
3
\(4\left( {2{\rm{\hat i}} + 2{\rm{\hat j}} - {\rm{\hat k}}} \right)\)
4
\(4\left( { - 2{\rm{\hat i}} - 2{\rm{\hat j}} + {\rm{\hat k}}} \right)\)