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Mathematics
Mathematics
Problem
14. Find the shortest distance between the lines whose vector equations are
r
⃗
=
(
i
^
+
2
j
^
+
3
k
^
)
+
λ
(
i
^
−
3
j
^
+
2
k
^
)
\vec{r}=(\hat{i}+2 \hat{j}+3 \hat{k})+\lambda(\hat{i}-3 \hat{j}+2 \hat{k})
r
=
(
i
^
+
2
j
^
+
3
k
^
)
+
λ
(
i
^
−
3
j
^
+
2
k
^
)
and
r
⃗
=
4
i
^
+
5
j
^
+
6
k
^
+
μ
(
2
i
^
+
3
j
^
+
k
^
)
\vec{r}=4 \hat{i}+5 \hat{j}+6 \hat{k}+\mu(2 \hat{i}+3 \hat{j}+\hat{k})
r
=
4
i
^
+
5
j
^
+
6
k
^
+
μ
(
2
i
^
+
3
j
^
+
k
^
)
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