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Find the coordinates of vectors which form the sides of ABCD

Find the coordinates of vectors which form the sides of ABCD

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Hi expert, please assist with this question without using cross-product. Kindly show your work. I appreciate your assistance

 

Question1: Let vectorsu = (u1, u2) and v = (v1, v2) be diagonals of parallelogram ABCD. a) Find the coordinates of vectors which form the sides of ABCD. b) Prove that the area of ABCD is equal to half of the area of parallelogram with two of its sides given by the vectors u and v. Hint: Draw pictures of the 2 parallelograms involved and indicate where u and v are on the parallelograms to assist you in understanding the questions. Note: The pictures that you draw do not constitute as answers. You must still write down the coordinates and the proof.
Transcribed Image Text:Question1: Let vectorsu = (u1, u2) and v = (v1, v2) be diagonals of parallelogram ABCD. a) Find the coordinates of vectors which form the sides of ABCD. b) Prove that the area of ABCD is equal to half of the area of parallelogram with two of its sides given by the vectors u and v. Hint: Draw pictures of the 2 parallelograms involved and indicate where u and v are on the parallelograms to assist you in understanding the questions. Note: The pictures that you draw do not constitute as answers. You must still write down the coordinates and the proof.
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As per our company policy, I am supposed to answer only one question at a time. For the rest please repost it again on the portal

(a)

In this question, we have given two vectors for the diagonal of the parallelogram ABCD

here 

AC=u

BD=v

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