Long Answer TypeProve, using vectors, that the altitudes of a triangle are concurrent.
OR
Prove that the perpendicular from the vertices to the opposite sides of a triangle are concurrent.
Let ABC be given triangle and H be the point of intersection of altitudes AL and BM. Join CH and produce it to meet BA in N.
Take H as origin.
Let 
be the position vectors of A, B, C respectively.
Since 
Again, 
...(2)
Adding (1) and (2), we get,
Short Answer TypeLong Answer TypeShort Answer Type
Switch
if 
if 
and 
then show that 
if 
