Question

a b c be three non zero vectors .if a.(b×c)=0 and b and c are not parallel..then prove a =mb +nc where m and n are some scalars.

Answer 1

ANSWER:-

Since, a+2b is collinear with c

a+2b=mc...(i)

Since b+3c is collinear with a

b+3c=na.....(ii)

Myltiplying Eq(ii) by 2 and subtracting Eq.(ii) from Eq.(i), we get

a−bc=mc−2na

On comparing, we get

m=−6;n=−

2

1

From Eq.(i), we have

a+2b=−6c

⇒a+b+6c=0