AP EAPCET 25-Aug-2021 Shift 2 Paper

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 Find a+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