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Mathematics
Problem
An incident ray is given by the vector
s
=
4
i
^
+
3
j
^
−
12
k
^
\mathbf{s}=4\,\hat{\mathbf{i}}+3\,\hat{\mathbf{j}}-12\,\hat{\mathbf{k}}
s
=
4
i
^
+
3
j
^
−
12
k
^
(in arbitrary units). The reflecting plane has a unit normal
n
^
=
1
3
(
i
^
+
j
^
+
k
^
)
\hat{\mathbf{n}}=\tfrac{1}{\sqrt{3}}(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}})
n
^
=
3
1
(
i
^
+
j
^
+
k
^
)
. Determine the vector of the reflected ray.
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