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.
233.In a triangle OAB , ∠AOB = 90°. If P and Q are the points of trisection of AB, prove that
Take O as origin, Let P divide AB in the ratio 1 : 2 Let Q divide AB in the ratio 2 : 1 L.H.S. = R.H.S. =
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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.
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