Given a, b and c are non zero vectors such that no two of these are collinear. a+2b is collinear with c and b+3c is collinear with a. To Finda+2b+6c Since, a+2b is collinear with c. ⇒ a+2b=mc ...(i) where m is non zero scalar. and b+3c=na ...(ii) Multiply by 2 in Eq. (ii) and subtracting from Eq. (i). a+2b−2b−6c=mc−2na a−6c=mc−2na On comparing both sides m=−6 and n=
−1
2
From Eq. (i), we get a+2b=mc a+2b=−6c ⇒ a+2b+6c=0