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Mathematics
Mathematics
Problem
If
P
P
P
be any point on the plane
l
x
+
m
y
+
n
z
=
p
lx + my + nz = p
l
x
+
m
y
+
n
z
=
p
and
Q
Q
Q
be a point on the line
O
P
OP
O
P
such that
O
P
⋅
O
Q
=
p
2
OP \cdot OQ = p^2
O
P
⋅
O
Q
=
p
2
, show that the locus of the point
Q
Q
Q
is
p
(
l
x
+
m
y
+
n
z
)
=
x
2
+
y
2
+
z
2
p(lx + my + nz) = x^2 + y^2 + z^2
p
(
l
x
+
m
y
+
n
z
)
=
x
2
+
y
2
+
z
2
.
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