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 xa n d vec y are two non-collinear vectors and A B C isa triangle with side lengths a ,b ,a n dc satisfying (20 a-15 b) vec x+(15b-12 c) vec y+(12 c-20 a)( vecx xx vec y)=0, then triangle A B C 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 x xx 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

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 vertices A, B, C of a triangle ABC, Show that the area of the triangle is (1)/(2) |vec(b) xx vec(c) + vec(c) xx vec(a) + vec(a) xx vec(b)|

If vec a ,\ vec b ,\ vec c are the position vectors of the vertices of an equilateral triangle whose orthocentre is the origin, then write the value of vec a+ vec b+ vec c

If veca , vec b , vec c are the position vectors of the vertices A ,B ,C of a triangle A B C , show that the area triangle A B Ci s1/2| vec axx vec b+ vec bxx vec c+ vec cxx vec a|dot Deduce the condition for points veca , vec b , vec c to be collinear.

If vec a ,\ vec b ,\ vec c are position vectors of the vertices of a triangle, then write the position vector of its centroid.

What is the angle between vec(a) and vec(b) : (i) Magnitude of vec(a) and vec(b) are 3 and 4 respectively. (ii) Area of triangle made by vec(a) and vec(b) is 10.

Let ABC be a triangle whose circumcentre is at P. If the position vectors of A, B, C and P are vec(a) , vec(b) , vec(c ) and (vec(a) + vec(b) + vec(c ))/(4) respectively, then the position vector of the orthocentre of this triangle is