222.Using vectors, prove that if two medians of a triangle ABC be equal, then it is an isosceles triangle.
Let BE and CF be two medians of ∆ABC. Take A an origin. Let Since E is mid-point of AC position vector of E is Similarly position vector of F is . Now, and From given condition,
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223.Using vectors, prove that the perpendicular bisectors of the sides of a triangle are concurrent.
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224.Prove that the median to the base of isosceles triangle is perpendicular to the base.
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Long Answer Type
225.If the median of the base of a triangle is perpendicular on the base, then prove that the triangle is an isosceles.
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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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Long Answer Type
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
position vector of E is 
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