Published by:
CGP EDU Academic Team
Published on: August 12, 2026
Using vectors, prove that the altitudes of a triangle are concurrent.
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
Let AD 
BC and BE 
AC. Let AD and BE meet at O. Join CO and produce it to meet AB at F.
Take O as the origin. Let 
be the position vectors of A, B and C respectively.
∴ 
= 
and 
= 
Now 
⇒ 
⇒ 
= 0
and 
⇒ 
⇒ 
These imply
and 
⇒ 
⇒ ( 
). 
= 0
⇒ 
⇒ CF 
AB
⇒ Altitudes of a Δ are concurrent.
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