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Mathematics
Mathematics
Problem
If
a
\mathbf{a}
a
is perpendicular to
b
\mathbf{b}
b
and
p
p
p
is non-zero scalar such that
p
r
+
(
r
⋅
b
)
a
=
c
p\mathbf{r} + (\mathbf{r} \cdot \mathbf{b})\mathbf{a} = \mathbf{c}
p
r
+
(
r
⋅
b
)
a
=
c
, then
r
\mathbf{r}
r
a.
[
r
a
c
]
=
0
[\mathbf{r} \mathbf{a} \mathbf{c}] = 0
[
rac
]
=
0
b.
p
2
r
=
p
a
−
(
c
⋅
a
)
b
p^2\mathbf{r} = p\mathbf{a} - (\mathbf{c} \cdot \mathbf{a})\mathbf{b}
p
2
r
=
p
a
−
(
c
⋅
a
)
b
c.
p
2
r
=
p
b
−
(
a
⋅
b
)
c
p^2\mathbf{r} = p\mathbf{b} - (\mathbf{a} \cdot \mathbf{b})\mathbf{c}
p
2
r
=
p
b
−
(
a
⋅
b
)
c
d.
p
2
r
=
p
c
−
(
b
⋅
c
)
a
p^2\mathbf{r} = p\mathbf{c} - (\mathbf{b} \cdot \mathbf{c})\mathbf{a}
p
2
r
=
p
c
−
(
b
⋅
c
)
a
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