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Mathematics
Mathematics
Problem
Find the acute angle between the lines with equations
r
=
(
1
0
4
)
+
λ
(
2
1
−
1
)
and
r
=
(
−
4
1
2
)
+
μ
(
1
3
−
5
)
.
\mathbf{r} = \begin{pmatrix} 1 \\ 0 \\ 4 \end{pmatrix} + \lambda \begin{pmatrix} 2 \\ 1 \\ -1 \end{pmatrix} \text{ and } \mathbf{r} = \begin{pmatrix} -4 \\ 1 \\ 2 \end{pmatrix} + \mu \begin{pmatrix} 1 \\ 3 \\ -5 \end{pmatrix}.
r
=
1
0
4
+
λ
2
1
−
1
and
r
=
−
4
1
2
+
μ
1
3
−
5
.
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