Let A B C be an equilateral triangle of side a . M and N are two points on the sides A B and A C respectively such that AN = K AC and AB =3 AM . If the vectors BN and CM are perpendicular, then K =

Step-by-step solution

Since, A B =3 A M , A N =K A C aligned & Now, C M B N =0 & ( A M - A C ) ( A N - A B )=0 & ( 1 3 A B - A C )(K A C - A B )=0 & K 3 A B A C --| A B |^2-K| A C |^2+ A C A B =0 & K a^2 6 - a^2 3 -K a^2+ a^2 2 =0 K= 1 5 aligned