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Mathematics
Mathematics
Problem
Find the shortest distance between the lines
r
⃗
1
=
(
6
i
^
+
2
j
^
+
2
k
^
)
+
λ
(
1
i
^
−
2
j
^
+
2
k
^
)
\vec{r}_1 = (6\hat{i} + 2\hat{j} + 2\hat{k}) + \lambda(1\hat{i} - 2\hat{j} + 2\hat{k})
r
1
=
(
6
i
^
+
2
j
^
+
2
k
^
)
+
λ
(
1
i
^
−
2
j
^
+
2
k
^
)
r
⃗
2
=
(
−
4
i
^
+
0
j
^
−
1
k
^
)
+
μ
(
3
i
^
−
2
j
^
−
2
k
^
)
\vec{r}_2 = (-4\hat{i} + 0\hat{j} - 1\hat{k}) + \mu(3\hat{i} - 2\hat{j} - 2\hat{k})
r
2
=
(
−
4
i
^
+
0
j
^
−
1
k
^
)
+
μ
(
3
i
^
−
2
j
^
−
2
k
^
)
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