Question

If ` vec a , vec b , vec c and vec d ` are the position vectors of points A, B, C, D such that no three of them are collinear and ` vec a + vec c = vec b + vec d ,` then ABCD is a
A. rhombus
B. rectangle
C. square
D. parallelogram

Answer 1

Correct Answer - D
We have,
`vec a + vec c = vec b + vec d `
`rArr vec b - vec a = vec c - vec d and vec d - vec a = vec c - vec b `
`rArr A vec B = D vec C and A vec D = B vec C `
`rArr ABCD ` is a parallelogram.