Question 3 - A-Level Maths

The points \(A , B\) and \(C\), with position vectors \(\mathbf { a } = 3 \mathbf { i } - 2 \mathbf { j } + \mathbf { k } , \mathbf { b } = \mathbf { i } + 4 \mathbf { j } + 5 \mathbf { k }\) and \(\mathbf { c } = - 2 \mathbf { i } + 3 \mathbf { j } + 3 \mathbf { k }\) respectively, lie on the plane \(\Pi\)
1. Find \(\overrightarrow { A B } \times \overrightarrow { A C }\)
2. Find an equation for \(\Pi\) in the form r.n \(= p\)
The point \(D\) has position vector \(8 \mathbf { i } + 7 \mathbf { j } + 5 \mathbf { k }\)
Determine the volume of the tetrahedron \(A B C D\)