1 Group 13
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Question 1.
Determine the vector
x
which satisfies the equality
1
2
a
-
2
x
=
b
-
5
x
, where
a
=
(
2
,
-
6
)
,
b
=
(
4
,
-
9
)
.
a)
x
=
(
-
1
,
2
)
b)
x
=
(
1
,
-
2
)
c)
x
=
(
1
,
4
)
d)
x
=
(
-
1
,
-
4
)
e)
x
=
(
1
,
-
1
)
Question 2.
Determine the straight line which passes through the point
[
2
,
1
]
and the intersection of lines
2
x
-
y
+
5
=
0
and
x
=
1
+
3
t
,
y
=
-
t
,
t
∈
ℝ
.
a)
y
-
1
=
0
b)
3
x
+
y
-
7
=
0
c)
does not exist.
d)
3
x
-
y
+
5
=
0
e)
-
x
-
2
y
+
4
=
0
Question 3.
The distance of the point
A
=
[
3
,
1
,
0
]
from the plane
x
+
2
y
+
z
-
1
=
0
is equal to
a)
7
5
6
b)
2
3
6
c)
1
5
6
d)
5
3
6
e)
7
3
6
Evaluate