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 30^ , then the value of |( a b ) c | is equal to

Step-by-step solution

aligned & | c - a |=2 2 & | c |^2+| a |^2-2( a c )=8 & | c |^2+9-2| c |=8 [ a c =| c | (given) ] & (| c |-1)^2=0 & | c |=1 aligned aligned & Now, |( a b ) c | & =| a b || c | 6 & =| a b |(1) ( 1 2 ) & = 3 2 [ a b =2 i -2 j + k ] aligned