A

Determine whether the following two lines are identical, parallel, intersecting or skew. \[\begin{aligned} a\colon x & = t, & & \\y & = -t, & & \\z & = 1 - t,\ t\in \mathbb{R} & & \end{aligned}\]\[\begin{aligned} b\colon x & = -s, & & \\y & = s, & & \\z & = -1 + s,\ s\in \mathbb{R} & & \end{aligned}\]

Given vectors \(\vec{a} = (2,2,-3)\), \(\vec{b} = (-1,0,1)\), \(\vec{c} = (0,-2,1)\), find the length of the vector \(\vec{u} =\vec{ a} - 2\vec{b} + 3\vec{c}\).

Given points \(A = [-3,2]\) and \(B = [1,y]\), find the values of \(y\) which ensure the length of the vector \(\overrightarrow{AB } \) equals \(5\).

Given vectors \(\vec{a}\), \(\vec{b}\), \(\vec{c}\), \(\vec{d}\), find \(\vec{a} +\vec{ b} +\vec{ c} +\vec{ d}\).