Home
Class 12
MATHS
If vec a , vec b , vec c , vec d are th...

If ` vec a` ,` vec b` ,` vec c` ,` vec d` are the position vector of point `A , B , C` and `D` , respectively referred to the same origin `O` such that no three of these point are collinear and ` vec a` + ` vec c` = ` vec b` + ` vec d` , than quadrilateral `A B C D` is a ;

A

square

B

rhombus

C

rectangle

D

parallelogram

Text Solution

Verified by Experts

The correct Answer is:
D
Given, `a+c=b+d`
`implies(1)/(2)(a+c)=(1)/(2)(b+d)`
Here, mid-points of AC and BD coincide, where AC and BD are diagonals. In addition, we know that, diagonals of a parallelogram bisect each other.
Hence, quadrilateral is parallelogram.
Promotional Banner

Similar Questions

Explore conceptually related problems

The position vector of the points A and B are respectively vec(a) and vec(b) . Find the position vectors of the points which divide AB in trisection.

If the position vector of a point A is vec a + 2 vec b and vec a divides AB in the ratio 2:3 , then the position vector of B, is

The position vectors of the points A, B, C are vec(a),vec(b) and vec( c ) respectively. If the points A, B, C are collinear then prove that vec(a)xx vec(b)+vec(b)xx vec( c )+vec( c )xxvec(a)=vec(0) .

Statement 1: Let vec a , vec b , vec ca n d vec d be the position vectors of four points A ,B ,Ca n dD and 3 vec a-2 vec b+5 vec c-6 vec d=0. Then points A ,B ,C ,a n dD are coplanar. Statement 2: Three non-zero, linearly dependent coinitial vector ( vec P Q , vec P Ra n d vec P S) are coplanar. Then vec P Q=lambda vec P R+mu vec P S ,w h e r elambdaa n dmu are scalars.

The position vectors of the points (1, -1) and (-2, m) are vec(a) and vec(b) respectively. If vec(a) and vec(b) are collinear then find the value of m.

If vec a , vec b are the position vectors of the points (1,-1),(-2,m), find the value of m for which vec aa n d vec b are collinear.

If the vectors vec a , vec b ,a n d vec c form the sides B C ,C Aa n dA B , respectively, of triangle A B C ,t h e n

Vectors drawn from the origin O to the points A , B and C are respectively vec a , vec b and 4veca- 3vecbdot find vec(AC) and vec(BC)dot

The position vectors of A, B,C and D are vec a , vec b , vec 2a+ vec 3b and vec a - vec 2b respectively. Show that vec (DB)=3 vec b -vec a and vec (AC) =vec a + vec 3b

The position vectors of two points A and B are respectively 6vec(a)+2vec(b) and vec(a)-3bar(b) . If the point C divides AB internally in the ratio 3 : 2 then the position vector of C is ……………