Show that the diagonals of a parallelogram are perpendicular if and only if it is a rhombus, i.e., its four sides have equal lengths. In vector notation, AC = AB + BC = a + b BD = BC + CD = b - a AC . The position vectors of D, E, F are respectively.Since Again, Adding (1) and (2), we get, perpendicular bisectors meet in a point. (b-a) = (b+a) . Let ABC be the given triangle and O be the point of intersection of perpendicular bisectors OD and OE of sides BC and CA respectively.Let F be mid-point of AB. From this is is easy to say that the diagonals are perpendicular. Buy Find arrow_forward. if it is given ∣ a ∣ = 2 2 : ∣ ∣ ∣ b ∣ ∣ ∣ = 3 and ( a , b ) = π / 4 is Calculus (MindTap Course List) 11th Edition. When we use vectors in this more general way, there is no reason to limit the number of components to three. Using vectors, prove that the diagonals of a rhombus are perpendicular. 11 - Proof Using vectors, prove that the diagonals of a... Ch. ... Ch. Hints. Example 2 Show that the diagonals of a rhombus are perpendicular to each other. For the following figure- The sides of a Rhombus are equal. First, assume Then. We have Using Vectors, prove that the diagonals of a parallelogram are perpendicular if and only if the parallelogram is a rhombus. (b-a) = b^2 - a^2 = 0 (as a =b). Ron Larson + 1 other. ... Use vectors to show that the diagonals of a rhombus are perpendicular. 3. A quadrilateral whose all sides, diagonals and angles are equal is a (a) square (b) trapezium (c) rectangle (d) rhombus asked Jul 30, 2020 in Quadrilaterals by Dev01 ( 51.7k points) quadrilaterals (Note: a rhombus is a parallelogram whose four sides all have the same lenth) I've got no idea how to do this problem and my TA isn't very clear in … Then we have the two diagonals are A + B and A − B. Prove by vector method that the Internal bisectors of the angles of a triangle are concurrent . BD = (a+b) . Publisher: Cengage Learning. Transcript. Thus AB = BC = CD = DA. 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