- Given that the point \(A\) has position vector \(x \mathbf { i } - \mathbf { j }\), the point B has position vector \(- 2 \mathbf { i } + y \mathbf { j }\) and \(\overrightarrow { A B } = - 3 \mathbf { i } + 4 \mathbf { j }\), find
a. the values of \(x\) and \(y\)
b. a unit vector in the direction of \(\overrightarrow { A B }\). - The line \(l _ { 1 }\) has equation \(2 x - 3 y = 9\)
The line \(l _ { 2 }\) passes through the points \(( 3 , - 1 )\) and \(( - 1,5 )\)
Determine, giving full reasons for your answer, whether lines \(l _ { 1 }\) and \(l _ { 2 }\) are parallel, perpendicular or neither.