Question 1211b

Vectors I: Basics, Dot and Cross Products

2011 Paper 1 Question 7ii Variant

Question

The vectors

{\mathbf{a}}

and

{\mathbf{b}}

are given by

\begin{align*} && \mathbf{a} = \begin{pmatrix} 4 p \\ p \\ - 8 p \end{pmatrix} \\ \textrm{ and } \quad && b = \begin{pmatrix} - 3 \\ - 2 \\ 5 \end{pmatrix}, \end{align*}

where

{p}

is a positive constant. Given that

{\mathbf{a}}

is a unit vector,

(a)

find the exact value of

{p,}

[2]

(b)

give a geometrical interpretation of

{\left|\mathbf{a}\cdot \mathbf{b}\right|,}

[1]

(c)

evaluate

{\mathbf{a}\times\mathbf{b}.}

[2]

Answer

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