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If is a tetrahedron such that
MATHEMATICS · Single correct · A Level · Mathematics · Vectors · Vectors
Problem
If
O
A
B
C
OABC
O
A
B
C
is a tetrahedron such that
O
A
2
+
B
C
2
=
O
B
2
+
C
A
2
=
O
C
2
+
A
B
2
OA^2 + BC^2 = OB^2 + CA^2 = OC^2 + AB^2
O
A
2
+
B
C
2
=
O
B
2
+
C
A
2
=
O
C
2
+
A
B
2
, then (1)
O
A
⊥
B
C
OA \perp BC
O
A
⊥
B
C
(2)
O
B
⊥
A
C
OB \perp AC
O
B
⊥
A
C
(3)
O
C
⊥
A
B
OC \perp AB
O
C
⊥
A
B
(4)
A
B
⊥
A
C
AB \perp AC
A
B
⊥
A
C
Related theory
Vector Operations
Vectors
Dot Product
Scalar product
Vector Algebra
Dot product of two vectors
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