Let a =2 i + j -2 k and b = i + j . Let c be a vector such that | c - a |=3 and |( a b ) c |=3 and the angle between c and a b is 30^ , 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 =30^ ...[Given] 30^ = |( a b ) c | | a b || c | aligned & 1 2 = 3 3 | c | & | c |=2 aligned aligned & Now, | c - a |=3 & | c |^2+| a |^2-2 a c =9 & 4+9-2 a c =9 & a c =2 aligned