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Mathematics
Mathematics
Problem
The distance between the line
r
=
2
i
−
2
j
+
3
k
+
λ
(
i
−
j
+
4
k
)
\mathbf{r} = 2\mathbf{i} - 2\mathbf{j} + 3\mathbf{k} + \lambda(\mathbf{i} - \mathbf{j} + 4\mathbf{k})
r
=
2
i
−
2
j
+
3
k
+
λ
(
i
−
j
+
4
k
)
and the plane
r
⋅
(
i
+
5
j
+
k
)
=
5
\mathbf{r} \cdot (\mathbf{i} + 5\mathbf{j} + \mathbf{k}) = 5
r
⋅
(
i
+
5
j
+
k
)
=
5
is a.
10
3
3
\frac{10}{3\sqrt{3}}
3
3
10
b.
10
3
\frac{10}{3}
3
10
c.
10
9
\frac{10}{9}
9
10
d.
10
3
\frac{10}{\sqrt{3}}
3
10
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