Parallel Vectors and Coefficients of $\mu$ I have a question that states the following
Given that c = 3i + 4j and d = i - 2j, find μ if μc + d is parallel to i + 3j
So I wrote the following
$$ c = \begin{pmatrix}  3\\ 4\\ \end{pmatrix}$$
$$ d = \begin{pmatrix}  1\\ -2\\ \end{pmatrix}$$
I then wrote 
$$ \mu \textbf{c} + \textbf{d} =\mu\begin{pmatrix}  3\\ 4\\ \end{pmatrix} + \begin{pmatrix}  1\\ -2\\ \end{pmatrix}$$
$$= \begin{pmatrix}  3\mu + 1\\ 4\mu-2\\ \end{pmatrix}$$
Now I thought that if this is parallel to i + 3j then from above, 
$$3\mu + 1 = 3(4\mu -2)$$
but the answer says that, in fact $$4(3\mu + 1) = 4\mu -2$$
I am confused. Why is this?
Wouldn't that imply that it is parallel to 3i + j?
The answer, strangely is given as such


Using your notation, we have a vector 
$$\mathbf a= \begin {pmatrix}a_1\\a_2 \end{pmatrix}=\begin {pmatrix}1\\3 \end{pmatrix}$$ so a  vector parallel to $\mathbf a$ is of the form
$$
\mathbf b =\begin {pmatrix}b_1\\b_2 \end{pmatrix}=\begin {pmatrix}b_1\\3b_1 \end{pmatrix}
$$
Apply this to 
$$ \mathbf b=\begin {pmatrix}b_1\\b_2 \end{pmatrix}=
\begin {pmatrix}3\mu+1\\4\mu -2 \end{pmatrix}
$$
we have
$$
b_2=3b_1 \iff 4\mu -2=3(3\mu +1)
$$
