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Mathematics
Mathematics
Problem
The vector equation of the plane through the point
(
2
,
1
,
−
1
)
(2, 1, -1)
(
2
,
1
,
−
1
)
and passing through the line of intersection of the plane
r
⋅
(
i
^
+
3
j
^
−
k
^
)
=
0
\mathbf{r} \cdot (\hat{i} + 3\hat{j} - \hat{k}) = 0
r
⋅
(
i
^
+
3
j
^
−
k
^
)
=
0
and
r
⋅
(
j
^
+
2
k
^
)
=
0
\mathbf{r} \cdot (\hat{j} + 2\hat{k}) = 0
r
⋅
(
j
^
+
2
k
^
)
=
0
, is a.
r
⋅
(
i
^
+
9
j
^
+
11
k
^
)
=
0
\mathbf{r} \cdot (\hat{i} + 9\hat{j} + 11\hat{k}) = 0
r
⋅
(
i
^
+
9
j
^
+
11
k
^
)
=
0
b.
r
⋅
(
i
^
+
9
j
^
+
11
k
^
)
=
6
\mathbf{r} \cdot (\hat{i} + 9\hat{j} + 11\hat{k}) = 6
r
⋅
(
i
^
+
9
j
^
+
11
k
^
)
=
6
c.
r
⋅
(
i
^
−
3
j
^
−
13
k
^
)
=
0
\mathbf{r} \cdot (\hat{i} - 3\hat{j} - 13\hat{k}) = 0
r
⋅
(
i
^
−
3
j
^
−
13
k
^
)
=
0
d. None of these
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