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Question 1.
For which values of a parameter
α
∈
ℝ
are the vectors
u
=
(
α
,
α
+
1
,
-
8
)
,
v
=
(
5
,
α
,
2
)
perpendicular?
a)
α
∈
{
-
2
,
8
}
b)
α
∈
{
-
2
,
-
8
}
c)
α
∈
{
2
,
8
}
d)
α
∈
{
2
,
-
8
}
e)
α
=
-
2
Question 2.
The pair of straight lines
c
x
=
1
+
2
t
,
y
=
2
+
t
,
t
∈
ℝ
, and
d
x
=
-
4
s
,
y
=
3
-
2
s
,
s
∈
ℝ
, are
a)
different parallels
b)
lines intersecting at
[
2
,
1
]
c)
lines intersecting at
[
3
,
-
1
]
d)
identical lines
e)
skew lines
Question 3.
Determine the deviation of the straight line
x
-
3
1
=
y
-
1
2
=
z
-
2
2
from the plane
2
x
-
5
y
+
5
z
=
0
.
a)
arcsin
(
6
27
)
b)
arcsin
(
7
27
)
c)
arcsin
(
5
27
)
d)
arcsin
(
6
37
)
e)
arcsin
(
6
17
)
Evaluate