Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
Prove that the lines
x
=
p
y
+
q
x = py + q
x
=
p
y
+
q
,
z
=
r
y
+
s
z = ry + s
z
=
r
y
+
s
and
x
=
p
′
y
+
q
′
x = p'y + q'
x
=
p
′
y
+
q
′
,
z
=
r
′
y
+
s
′
z = r'y + s'
z
=
r
′
y
+
s
′
are perpendicular, if
p
p
′
+
r
r
′
+
1
=
0
pp' + rr' + 1 = 0
p
p
′
+
r
r
′
+
1
=
0
.
Browse the problem library