Question

Find the position vector of d and verify that the parallelogram is a rhombus.

Answer 1

Suppose a parallelogram ABCD in which vector 'a' is in vertical direction and vector 'b' in horizontal direction. An intersecting point E lies in b/w C, D such that DE: EC= 1: 2

(i) Vect('DC')=Vect('AB')= Vect('a')

(ii) Vect('CB')=Vect('-AD')= Vect('-b')

(iii) Vect('DE')=1/3 Vect('DC')= 1/3 Vect('a')

(iv) Vect('BE')=Vect('BC')+ Vect('CE')= Vect('b')+ Vect('CE')

Vect('CE')=2/3 Vect('CD')= -2/3 Vect('DC')= -2/3 Vect('A')

Therefore; Vect('BE')= Vect('b') +(-2/3 Vect('a'))

Vect('BE')= Vect('b') -2/3 Vect('a')