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Mathematics
Mathematics
Problem
8. Find the angle between the following pairs of lines: (i) $ vec{r}=2 hat{i}-5 hat{j}+ hat{k}+ lambda(3 hat{i}+2 hat{j}+6 hat{k})$ and
r
⃗
=
7
i
^
−
6
k
^
+
μ
(
i
^
+
2
j
^
+
2
k
^
)
\vec{r}=7 \hat{i}-6 \hat{k}+\mu(\hat{i}+2 \hat{j}+2 \hat{k})
r
=
7
i
^
−
6
k
^
+
μ
(
i
^
+
2
j
^
+
2
k
^
)
(ii)
r
⃗
=
3
i
^
+
j
^
−
2
k
^
+
λ
(
i
^
−
j
^
−
2
k
^
)
\vec{r}=3 \hat{i}+\hat{j}-2 \hat{k}+\lambda(\hat{i}-\hat{j}-2 \hat{k})
r
=
3
i
^
+
j
^
−
2
k
^
+
λ
(
i
^
−
j
^
−
2
k
^
)
and
r
⃗
=
2
i
^
−
j
^
−
56
k
^
+
μ
(
3
i
^
−
5
j
^
−
4
k
^
)
\vec{r}=2 \hat{i}-\hat{j}-56 \hat{k}+\mu(3 \hat{i}-5 \hat{j}-4 \hat{k})
r
=
2
i
^
−
j
^
−
56
k
^
+
μ
(
3
i
^
−
5
j
^
−
4
k
^
)
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