Let a =2 i + j -2 k , b = i + j and c be a vector such that | c - a |=4, |( a b ) c |=3 and the angle between c and a b is 6 , then a c is equal to

Step-by-step solution

array ll & a =2 i + j -2 k , b = i + j & | a |= 4+1+4 =3 & a b = | array ccc i & j & k 2 & 1 & -2 1 & 1 & 0 array |=2 i -2 j + k & | a b |= 4+4+1 =3 array Angle between c and a b is 6 [Given] aligned & 6 = |( a b ) c | | a b | c | & 1 2 = 3 3 | c | | c |=2 aligned Now, | c - a |=4 .. [Given] aligned & | c |^2+| a |^2-2 a c =16 & 4+9-2 a c=16 & a c= -3 2 aligned