If `vec(AO)+vec(OB)=vec(BO)+vec(OC)` then A,B,C,D form a/an (A) equilaterla triangle (B) righat angled triangle (C) isosceles triangle (D) straighat line

If | vec AO + vec OB | = | vec BO + vec OC |, then A, B, C form

If vec AO+vec OB=vec BO+vec OC, prove that A,B,C are collinear points.

If vec x and vec y are two non-collinear vectors and ABC isa triangle with side lengths a,b, and satisfying (20a-15b)vec x+(15b-12c)vec y+(12c-20a)(vec xxvec y)=0 then triangle ABC is a.an acute-angled triangle b.an obtuse- angled triangle c.a right-angled triangle d.an isosceles triangle

If vec xa n d vec y are two non-collinear vectors and a, b, and c represent the sides of a A B C satisfying (a-b) vec x+(b-c) vec y+(c-a)( vec xxx vec y)=0, then A B C is (where vec xxx vec y is perpendicular to the plane of xa n dy ) a. an acute-angled triangle b. an obtuse-angled triangle c. a right-angled triangle d. a scalene triangle

if vec Ao+vec OB=vec BO+vec OC, than prove that B is the midpoint of AC.

Let vec a,vec b,vec c form sides BC,CA and AB respectively of a triangle ABC then

The position vectors of the vertices A ,Ba n dC of a triangle are three unit vectors vec a , vec b ,a n d vec c , respectively. A vector vec d is such that vecd dot vec a= vecd dot vec b= vec d dot vec ca n d vec d=lambda( vec b+ vec c)dot Then triangle A B C is a. acute angled b. obtuse angled c. right angled d. none of these

If vec a,vec b,vec c are the position vectors of the vertices of an equilateral triangle whose orthocenter is at the origin,then

If vec AO+vec OB=vec BO+vec OC, then A,quad B nad C are (where O is the origin) a.coplanar b. collinear c.non-collinear d.none of these

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.