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Mathematics
Mathematics
Problem
Let
r
(
t
)
\mathbf r(t)
r
(
t
)
and
s
(
t
)
\mathbf s(t)
s
(
t
)
be differentiable vector-valued functions such that
r
(
t
)
⋅
s
(
t
)
=
0
\mathbf r(t)\cdot\mathbf s(t)=0
r
(
t
)
⋅
s
(
t
)
=
0
for all
t
t
t
. Which of the following must hold for every
t
t
t
? a)
r
′
(
t
)
⋅
s
(
t
)
=
0
\mathbf r'(t)\cdot\mathbf s(t)=0
r
′
(
t
)
⋅
s
(
t
)
=
0
b)
r
′
(
t
)
⋅
s
(
t
)
+
r
(
t
)
⋅
s
′
(
t
)
=
0
\mathbf r'(t)\cdot\mathbf s(t)+\mathbf r(t)\cdot\mathbf s'(t)=0
r
′
(
t
)
⋅
s
(
t
)
+
r
(
t
)
⋅
s
′
(
t
)
=
0
c)
r
′
(
t
)
⋅
s
(
t
)
−
r
(
t
)
⋅
s
′
(
t
)
=
0
\mathbf r'(t)\cdot\mathbf s(t)-\mathbf r(t)\cdot\mathbf s'(t)=0
r
′
(
t
)
⋅
s
(
t
)
−
r
(
t
)
⋅
s
′
(
t
)
=
0
d)
r
′
(
t
)
⋅
s
′
(
t
)
=
0
\mathbf r'(t)\cdot\mathbf s'(t)=0
r
′
(
t
)
⋅
s
′
(
t
)
=
0
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