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Question 1210
Vectors I: Basics, Dot and Cross Products
2010 Paper 1 Question 1 Variant
Question
Generate new
The position vectors
a
{\mathbf{a}}
a
and
b
{\mathbf{b}}
b
are given by
a
=
(
4
p
0
−
3
p
)
and
b
=
(
−
4
−
3
0
)
,
\begin{align*} && a=\begin{pmatrix} 4 p \\ 0 \\ - 3 p \end{pmatrix} \\ \textrm{and} \quad && b = \begin{pmatrix} - 4 \\ - 3 \\ 0 \end{pmatrix}, \end{align*}
and
a
=
4
p
0
−
3
p
b
=
−
4
−
3
0
,
where
p
>
0.
{p>0.}
p
>
0.
It is given that
∣
a
∣
=
∣
b
∣
.
{|\mathbf{a}| = |\mathbf{b}|.}
∣
a
∣
=
∣
b
∣.
(i)
Find the exact value of
p
.
{p.}
p
.
[2]
(ii)
Evaluate
(
a
+
b
)
⋅
(
a
−
b
)
.
{(\mathbf{a}+\mathbf{b})\cdot(\mathbf{a}-\mathbf{b}).}
(
a
+
b
)
⋅
(
a
−
b
)
.
[3]
Answer
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