Question 1210

Vectors I: Basics, Dot and Cross Products

2010 Paper 1 Question 1 Variant

Question

The position vectors

{\mathbf{a}}

and

{\mathbf{b}}

are given by

\begin{align*} && a=\begin{pmatrix} p \\ 2 p \\ - 2 p \end{pmatrix} \\ \textrm{and} \quad && b = \begin{pmatrix} - 8 \\ 1 \\ - 4 \end{pmatrix}, \end{align*}

where

{p>0.}

It is given that

{|\mathbf{a}| = |\mathbf{b}|.}

(i)

Find the exact value of

{p.}

[2]

(ii)

Evaluate

{(\mathbf{a}+\mathbf{b})\cdot(\mathbf{a}-\mathbf{b}).}

[3]