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Mathematics
Mathematics
Problem
Identify the correct expression for the reflected ray vector
v
r
\mathbf{v}_r
v
r
when an incident ray with vector
v
\mathbf{v}
v
strikes a plane whose unit normal is
n
^
\hat n
n
^
. a)
v
r
=
v
−
(
v
⋅
n
^
)
n
^
\mathbf{v}_r = \mathbf{v} - (\mathbf{v}\cdot\hat n)\,\hat n
v
r
=
v
−
(
v
⋅
n
^
)
n
^
b)
v
r
=
v
+
2
(
v
⋅
n
^
)
n
^
\mathbf{v}_r = \mathbf{v} + 2\,(\mathbf{v}\cdot\hat n)\,\hat n
v
r
=
v
+
2
(
v
⋅
n
^
)
n
^
c)
v
r
=
v
−
2
(
v
⋅
n
^
)
n
^
\mathbf{v}_r = \mathbf{v} - 2\,(\mathbf{v}\cdot\hat n)\,\hat n
v
r
=
v
−
2
(
v
⋅
n
^
)
n
^
d)
v
r
=
−
v
+
2
(
v
⋅
n
^
)
n
^
\mathbf{v}_r = -\mathbf{v} + 2\,(\mathbf{v}\cdot\hat n)\,\hat n
v
r
=
−
v
+
2
(
v
⋅
n
^
)
n
^
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