If `P` is a point and `A B C D` is a quadrilateral and ` vec A P+ vec P B+ vec P D= vec P C` , show that `A B C D` is a parallelogram.

A B C D is a quadrilateral. Find the sum the vectors vec B A , vec B C , and vec D A .

A B C D is a quadrilateral. Find the sum the vectors vec B A , vec B C , and vec D A .

ABC is a triangle and P any point on BC. if vec P Q is the sum of vec A P + vec P B + vec P C , show that ABPQ is a parallelogram and Q , therefore , is a fixed point.

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

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

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

A B C D is a parallelogram. P is a point on A D such that A P=1/3A D and Q is a point on B C such that C Q=1/3B P . Prove that A Q C P is a parallelogram.

A B C D E is pentagon, prove that vec A B+ vec A E+ vec B C+ vec D C+ vec E D+ vec A C=3 vec A C