1 Group 2
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Question 1.
For which values of a parameter
α
∈
ℝ
are the vectors
u
=
(
2
,
α
,
-
8
)
,
v
=
(
α
+
2
,
2
,
α
-
1
)
perpendicular?
a)
α
=
-
1
b)
α
=
3
c)
for none
α
d)
α
=
1
e)
α
=
-
3
Question 2.
The straight lines
2
x
+
3
y
+
5
=
0
and
3
x
-
2
y
+
3
=
0
are
a)
different parallels
b)
intersecting lines not perpendicular
c)
identical straight lines
d)
skew lines
e)
perpendicular intersecting straight lines
Question 3.
The orthogonal projection of the point
A
=
[
2
,
3
,
4
]
onto the straight line
X
=
[
0
,
0
,
0
]
+
t
(
1
,
1
,
1
)
,
t
∈
ℝ is
a)
[
3
,
3
,
3
]
b)
[
3
,
2
,
1
]
c)
[
1
,
1
,
1
]
d)
[
1
,
2
,
3
]
e)
[
2
,
2
,
2
]
Evaluate