If `Da n dE` are the mid-points of sides `A Ba n dA C` of a triangle `A B C` respectively, show that ` vec B E+ vec D C=3/2 vec B Cdot`

If D and E are the mid-points of sides AB and AC of a triangle ABC respectively, show that vec BE+vec DC=(3)/(2)vec BC

If O is a point in space, A B C is a triangle and D , E , F are the mid-points of the sides B C ,C A and A B respectively of the triangle, prove that vec O A + vec O B+ vec O C= vec O D+ vec O E+ vec O Fdot

If D ,E ,F are the mid-points of the sides B C ,C Aa n dA B respectively of a triangle A B C , prove by vector method that A r e aof D E F=1/4(a r e aof A B C)dot

D ,\ E ,\ F are the mid-point of the sides B C ,\ C A\ a n d\ A B respectively of A B Cdot Then D E F is congruent to triangle. A B C (b) AEF (c) B F D ,\ C D E (d) A F E ,\ B F D ,\ C D E

A ,B ,Ca n dD have position vectors vec a , vec b , vec ca n d vec d , respectively, such that vec a- vec b=2( vec d- vec c)dot Then a. A Ba n dC D bisect each other b. B Da n dA C bisect each other c. A Ba n dC D trisect each other d. B Da n dA C trisect each other

If A, B, C, D be any four points and E and F be the middle points of AC and BD respectively, then A vec(B) + C vec(B) +C vec (D) + vec(AD) is equal to

In a triangle OAC, if B is the mid point of side AC and vec O A= vec a , vec O B= vec b , then what is vec O C ?

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 are the position vectors of the vertices A,B,C of a triangle ABC, show that the area triangle ABCis(1)/(2)|vec a xxvec b+vec b xxvec c+vec c xxvec a| Deduce the condition for points vec a,vec b,vec c to be collinear.

vec a,vec b and vec c are the position vectors of points A,B and C respectively,prove that: vec a_(vec a)xvec b+vec bxvec c+vec cxvec a is vector perpendicular to the plane of triangle ABC.