Let →a = 2^i + ^j − ^k and →b = ^i + ^j. Let →c be a vector such that |→c − →a| = 3, |(→a × →b) × →c| = 3 and the angle between →c and →a × →b be 30°. Then →a ⋅ →c is equal to.

Given that:|(¯aׯb)ׯc|=3We can have|¯aׯb||¯c| sin30∘=3Thus we get,|¯aׯb||¯c|=6Now, we can verify that¯aׯb=2i𕒶j+kHence,¯aׯb=√4+4+1=3,|¯c|=2Now,|¯c−¯a|=2From Questionand|¯c−¯a|2=|¯c|2+|¯a|2𕒶¯c⋅¯a=9=4+9𕒶¯c⋅¯a=9Hence,2¯a⋅¯c=4¯a⋅¯c=2