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Mathematics
Mathematics
Problem
Consider a plane
x
+
y
−
z
=
1
x + y - z = 1
x
+
y
−
z
=
1
and the point
A
(
1
,
2
,
−
3
)
A(1, 2, -3)
A
(
1
,
2
,
−
3
)
. A line
L
L
L
has the equation
x
=
1
+
3
r
x = 1 + 3r
x
=
1
+
3
r
,
y
=
2
−
r
y = 2 - r
y
=
2
−
r
,
z
=
3
+
4
r
z = 3 + 4r
z
=
3
+
4
r
The coordinate of a point
B
B
B
of line
L
L
L
, such that
A
B
AB
A
B
is parallel to the plane, is a.
(
10
,
−
1
,
15
)
(10, -1, 15)
(
10
,
−
1
,
15
)
b.
(
−
5
,
4
,
−
5
)
(-5, 4, -5)
(
−
5
,
4
,
−
5
)
c.
(
4
,
1
,
7
)
(4, 1, 7)
(
4
,
1
,
7
)
d.
(
−
8
,
5
,
−
9
)
(-8, 5, -9)
(
−
8
,
5
,
−
9
)
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