225.If the median of the base of a triangle is perpendicular on the base, then prove that the triangle is an isosceles.
Let ABC be a triangle in which the median AD is perpendicular to base BC. Take A as origin. Let be position vectors of B and C so that . Since D is mid-point of BC
position vector of D is i.e., Also, Since
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226.(i) Prove that cos (α + β) )= cos α cos β – sin α sin β. (ii) Prove that cos (α – p) = cos α cos β + sin α sin β.
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227.Prove that the diagonals of a rectangle are perpendicular if and only if the rectangle is a square.
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228.Using vectors, prove that a parallelogram whose diagonals are equal is a rectangle.
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229.Prove using vectors: The quadrilateral obtained by joining mid-points of adjacent sides of a rectangle is a rhombus.
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230.Show that the angle between two diagonals of a cube is
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Long Answer Type
be position vectors of B and C so that 
.
position vector of D is 
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