Let a , b and c be unit vectors such that a b =0= a c and the acute angle between b and c is 3 , then | a b - a c | is equal to

Step-by-step solution

Given, | a |=| b |=| c |=1 and a b =0= a c angle between b and c = 3 To find, | a b - a c | Given that, a b =0 and a c =0 a ( b - c )=0 The angle between a and ( b - c ) is 2 . Now, | a b - a c |=| a ( b - c )|=| a || b - c | 90^ ...(i) | b - c |^2=| b |^2+| c |^2-2 b c aligned & =1+1-2 (| b || c | 3 ) & =2-2 (1 1 1 2 ) aligned | b - c |^2=1 | b - c |=1 From Eq. (i), we get | a b - a c |=1