Let a =2 i + j -2 k and b = i + j . If c is a vector such that a c =| c |,| c - a |=2 2 and the angle between a b and c is 60^ . Then |( a b ) c |=

Step-by-step solution

aligned & 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 . Also | a |= 4+1+4 =3 & c - a =2 2 ( c - a )^2=8 & c - a =2 2 ( c - a )^2=8 & | c |^2+| a |^2=2 c a =8 & | c |^2+9-2| c |=8 & | c |^2-2| c |+1=0 (| c |-1)^2=0 | c |=1 & |( a b ) c |=| a b | | c | 60^ =(3)(1) ( 3 2 )= 3 3 2 aligned