Question: Using dot or scalar product, prove that the diagonals of a rhombus are perpendicular to each other. First, assume Then. 11 - … Solution: If the parallelogram with vertices 0; A; B; A + B is a rhombus, then kAk = kBk; and the diagonals … (b-a) = b^2 - a^2 = 0 (as a =b). Using Vectors, prove that the diagonals of a parallelogram are perpendicular if and only if the parallelogram is a rhombus. Publisher: Cengage Learning. Algebra and Trigonometry (8th Edition) Edit edition. Example 2 Show that the diagonals of a rhombus are perpendicular to each other. Calculus (MindTap Course List) 11th Edition. 11 - Proof Using vectors, prove that the diagonals of a... Ch. Using vectors, prove that the diagonals of a rhombus are perpendicular. Thus AB = BC = CD = DA. We have Then we have the two diagonals are A + B and A − B. Buy Find arrow_forward. Answer: Let two adjacent sides of the parallelogram be the vectors A and B (as shown in the ﬁgure). Problem 89E from Chapter 8.4: PROOF Use vectors to prove that the diagonals of a rhombus a... Get solutions 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. View Answer The length of longer diagonal of the parallelogram on 5 a + 2 b and a − 3 b . if it is given ∣ a ∣ = 2 2 : ∣ ∣ ∣ b ∣ ∣ ∣ = 3 and ( a , b ) = π / 4 is The position vectors of D, E, F are respectively.Since Again, Adding (1) and (2), we get, perpendicular bisectors meet in a point. 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 BD = (a+b) . (b-a) = (b+a) . ... Use vectors to show that the diagonals of a rhombus are perpendicular. From this is is easy to say that the diagonals are perpendicular. Show that is true for any vectors u, v, and w. (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 … 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. Transcript. For the following figure- The sides of a Rhombus are equal. Ron Larson + 1 other. ... Ch. In vector notation, AC = AB + BC = a + b BD = BC + CD = b - a AC . Prove by vector method that the Internal bisectors of the angles of a triangle are concurrent . 3. Hints. Let u and v be nonzero vectors, and let denote the angle between them. When we use vectors in this more general way, there is no reason to limit the number of components to three. Proof Use vectors to prove that the diagonals of a rhombus are perpendicular. Join O to F.Take O as origin.Let be the position vectors of A, B, C respectively. Proof. 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