224.Prove that the median to the base of isosceles triangle is perpendicular to the base.
Let ABC be an isosceles triangle with AB = AC and let AD be the median to the base BC. Then D is the middle point of BC. Take A as origin. Let be position vectors of B and C respectively with respect to origin A such that Then position vector of D w.r.t A is Now,
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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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Short Answer Type
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
Short Answer Type
Long Answer Type
be position vectors of B and C respectively with respect to origin A such that 
Then position vector of D w.r.t A is 
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