Đáp án:
$\begin{array}{l}
a)\left( d \right):y = - x + 4\\
a = - 1;b = 4\\
\left( {{d_1}} \right):y = x - 1\\
{a_1} = 1;{b_1} = - 1\\
Do:a.{a_1} = \left( { - 1} \right).1 = - 1\\
\Leftrightarrow \left( d \right) \bot \left( {{d_1}} \right)
\end{array}$
Vậy (d) cắt đường thẳng đã cho.
$\begin{array}{l}
b)\left( {d'} \right)//\left( d \right)\\
\Leftrightarrow \left\{ \begin{array}{l}
- 1 = m + 1\\
4 \ne m - 1
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
m = - 2\\
m \ne 5
\end{array} \right.\\
\Leftrightarrow m = - 2\\
Vậy\,m = - 2
\end{array}$
