- The line \(l _ { 1 }\) has equation
$$\frac { x - 1 } { 2 } = \frac { y + 1 } { - 1 } = \frac { z - 4 } { 3 }$$
The line \(l _ { 2 }\) has equation
$$\mathbf { r } = \mathbf { i } + 3 \mathbf { k } + t ( \mathbf { i } - \mathbf { j } + 2 \mathbf { k } )$$
where \(t\) is a scalar parameter.
- Show that \(l _ { 1 }\) and \(l _ { 2 }\) lie in the same plane.
- Write down a vector equation for the plane containing \(l _ { 1 }\) and \(l _ { 2 }\)
- Find, to the nearest degree, the acute angle between \(l _ { 1 }\) and \(l _ { 2 }\)