Time allowed: 20 minutes.
1. (2 marks)
Find the equation of the plane
x
+ 3
y
−
2
z
= 12 in parametric and point-normal form.
2. (2 marks)
Find the points of intersection (if any) of the line
˜
x
=
−
9
−
3
+
λ
4
3
for
λ
∈
R
and the circle with radius 5 and centre
7
9
.
3. (2 marks)
Find the volume of the parallelepiped spanned by
⎛
⎝
−
1
−
2
0
⎞
⎠
,
⎛
⎝
1
−
2
−
1
⎞
⎠
and
⎛
⎝
−
3
−
1
−
2
⎞
⎠
.
4. (4 marks)
Suppose that
A
=
⎡
⎢
⎢
⎢
⎢
⎣
50
0
0
1
21
4
a
37
102
20
−
3
0
0
0
−
1
40
0
−
2
1
108
2
0
0
1
12
⎤
⎥
⎥
⎥
⎥
⎦
.
(a) Without doing any calculations, state a value of
a
for which
A
is not invertible.
(b) If det(
A
) =
−
84, determine the value of
a
.
Week 10
Tuesday 10-11 Class

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