Let a, b and c are 3 non zero vectors such that no 2 of these are collinear. If vector a + 2b is collinear…
Let a, b and c are 3 non zero vectors such that no 2 of these are collinear. If vector a + 2b is collinear with c and b + 3c is collinear with a (l being some non zero scalar) then
a + 2b + 6c equals
$\lambda \mathbf{a}$
$\lambda \mathbf{b}$
$\lambda \mathbf{c}$
0
Solution
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.
$\Rightarrow \quad \mathbf{a}+2 \mathbf{b}=m \mathbf{c}...(i)$
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 $n=\frac{-1}{2}$
From Eq. (i), we get a + 2b = mc
a + 2b = − 6c
$\Rightarrow \quad a+2 b+6 c=0$