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Mathematics
Mathematics
Problem
If
a
⃗
\vec{a}
a
,
b
⃗
\vec{b}
b
,
c
⃗
\vec{c}
c
are three non-coplanar and
p
⃗
\vec{p}
p
,
q
⃗
\vec{q}
q
,
r
⃗
\vec{r}
r
are reciprocal vectors to
a
⃗
\vec{a}
a
,
b
⃗
\vec{b}
b
and
c
⃗
\vec{c}
c
respectively, then
(
l
a
⃗
+
m
b
⃗
+
n
c
⃗
)
⋅
(
l
p
⃗
+
m
q
⃗
+
n
r
⃗
)
(l\vec{a} + m\vec{b} + n\vec{c}) \cdot (l\vec{p} + m\vec{q} + n\vec{r})
(
l
a
+
m
b
+
n
c
)
⋅
(
l
p
+
m
q
+
n
r
)
is equal to : (where
l
l
l
,
m
m
m
,
n
n
n
are scalars) (A)
l
2
+
m
2
+
n
2
l^2 + m^2 + n^2
l
2
+
m
2
+
n
2
(B)
l
m
+
m
n
+
n
l
lm + mn + nl
l
m
+
mn
+
n
l
(C) 0 (D) None of these
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