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Mathematics
Mathematics
Problem
Equation of the plane that contains the lines
r
=
(
i
^
+
j
^
)
+
λ
(
i
^
+
2
j
^
−
k
^
)
\mathbf{r} = (\hat{i} + \hat{j}) + \lambda(\hat{i} + 2\hat{j} - \hat{k})
r
=
(
i
^
+
j
^
)
+
λ
(
i
^
+
2
j
^
−
k
^
)
and,
r
=
(
i
^
+
j
^
)
+
μ
(
−
i
^
+
j
^
−
2
k
^
)
\mathbf{r} = (\hat{i} + \hat{j}) + \mu(-\hat{i} + \hat{j} - 2\hat{k})
r
=
(
i
^
+
j
^
)
+
μ
(
−
i
^
+
j
^
−
2
k
^
)
is a.
r
⋅
(
2
i
^
+
j
^
−
3
k
^
)
=
−
4
\mathbf{r} \cdot (2\hat{i} + \hat{j} - 3\hat{k}) = -4
r
⋅
(
2
i
^
+
j
^
−
3
k
^
)
=
−
4
b.
r
×
(
−
i
^
+
j
^
+
k
^
)
=
0
\mathbf{r} \times (-\hat{i} + \hat{j} + \hat{k}) = 0
r
×
(
−
i
^
+
j
^
+
k
^
)
=
0
c.
r
⋅
(
−
i
^
+
j
^
+
k
^
)
=
0
\mathbf{r} \cdot (-\hat{i} + \hat{j} + \hat{k}) = 0
r
⋅
(
−
i
^
+
j
^
+
k
^
)
=
0
d. None of the above
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