Home
Class 12
MATHS
vec a, vec b, vec c, vec d are the posit...

`vec a`, `vec b`, `vec c`, `vec d` are the position vectors of the four distinct points A, B, C, D respectively. If `vec b-vec a=vec c- vec d`, then show that ABCD is a parallelogram.

Text Solution

Verified by Experts

The correct Answer is:
`vec(b)-vec(a)=vec(c )-vec(d)rArr vec(a)-vec(b)=vec(d)-vec(c ) rArr vec(QP)=vec(RS)`; etc.
Promotional Banner

Topper's Solved these Questions

  • VECTOR ALGEBRA

    MODERN PUBLICATION|Exercise EXERCISE 10 (d) Long Answer Type Questions (II)|1 Videos

  • VECTOR ALGEBRA

    MODERN PUBLICATION|Exercise EXERCISE 10 (e ) Short Answer Type Questions|28 Videos

  • VECTOR ALGEBRA

    MODERN PUBLICATION|Exercise EXERCISE 10 (c ) Long Answer Type Questions (II)|3 Videos

  • THREE DIMENSIONAL GEOMETRY

    MODERN PUBLICATION|Exercise CHAPTER TEST 11|11 Videos

Similar Questions

Explore conceptually related problems

Let vec a,vec b,vec c,vec d be the position vectors of the four distinct points A,B,C,D. If vec b-vec a=vec a-vec d, then show that ABCD is parallelogram.

If vec a,vec b,vec c are the position vectors of points A,B,C and D respectively such that (vec a-vec d)*(vec b-vec c)=(vec b-vec d)*(vec c-vec a)=0 then D is the

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

If vec a,vec b,vec c are position vectors o the point A,B, and C respectively,write the value of vec AB+vec BC+vec AC

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

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 prove that quadrilateral A B C D is a parallelogram.

If vec(b) and vec(c) are the position vectors of the points B and C respectively, then the position vector of the point D such that vec(BD) = 4 vec(BC) is

If vec(b) and vec(c ) are the position vectors of the points B and C respectively, then the position vector of the point D such that vec(BD)= 4 vec(BC) is

If vec a,vec b,vec c and vec d are the position vectors of the points A,B,C and D respectively in three dimensionalspace no three of A,B,C,D are collinear and satisfy the relation 3vec a-2vec b+vec c-2vec d=0, then

vec a, vec b, vec c, vec d are four distinct vectors satisfying the conditions vec a xxvec b = vec c xxvec d and vec a xxvec c = vec b xxvec d then prov that vec a * vec b + vec c.vec d! = vec a * vec c + vec b.vec d