Prove, 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.
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232.Show that the diagonals of a rhombus bisect each other at right angles.
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233.In a triangle OAB , ∠AOB = 90°. If P and Q are the points of trisection of AB, prove that
234.In a tetrahedron, if two pairs of opposite edges are perpendicular, then the third pair is also perpendicular to each other and the sum of the sequares of two opposite edges is the same for each pair.
Let ABCD be the tetrahedron. Take D as origin, are position vectors of A, B, C respectively with D as origin. Let DA and CB be perpendicular. Let DB and AC be perpendicular.