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Mathematics
Mathematics
Problem
An incident ray is represented by the vector
v
=
3
i
^
−
4
j
^
\mathbf{v}=3\hat i-4\hat j
v
=
3
i
^
−
4
j
^
(units arbitrary). It strikes a plane whose unit normal is
n
^
=
1
2
(
0
i
^
+
1
j
^
+
1
k
^
)
\hat n=\dfrac{1}{\sqrt{2}}\,(0\hat i+1\hat j+1\hat k)
n
^
=
2
1
(
0
i
^
+
1
j
^
+
1
k
^
)
. Find the reflected ray vector
v
r
\mathbf{v}_r
v
r
. a)
3
i
^
+
4
j
^
+
0
k
^
3\hat i+4\hat j+0\hat k
3
i
^
+
4
j
^
+
0
k
^
b)
3
i
^
+
0
j
^
+
4
k
^
3\hat i+0\hat j+4\hat k
3
i
^
+
0
j
^
+
4
k
^
c)
3
i
^
−
8
j
^
−
4
k
^
3\hat i-8\hat j-4\hat k
3
i
^
−
8
j
^
−
4
k
^
d)
3
i
^
−
2
j
^
+
2
k
^
3\hat i-2\hat j+2\hat k
3
i
^
−
2
j
^
+
2
k
^
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