A point `O` is the centre of a circle circumscribed about a triangle`A B Cdot` Then ` vec O Asin2A+ vec O Bsin2B+ vec O Csin2C` is equal to

If D is the mid-point of the side B C of a triangle A B C , prove that vec A B+ vec A C=2 vec A Ddot

If S is the cirucmcentre, G the centroid, O the orthocentre of a triangle ABC, then vec(SA) + vec(SB) + vec(SC) is:

A B C D is a quadrilateral and E and the point intersection of the lines joining the middle points of opposite side. Show that the resultant of vec O A , vec O B , vec O Ca n d vec O D is equal to 4 vec O E , where O is any point.

A sector O A B O of central angle theta is constructed in a circle with centre O and of radius 6. The radius of the circle that is circumscribed about the triangle O A B , is 6costheta/2 (b) 6sectheta/2 3sectheta/2 (d) 3(costheta/2+2)

If O A B C is a tetrahedron where O is the orogin anf A ,B ,a n dC are the other three vertices with position vectors, vec a , vec b ,a n d vec c respectively, then prove that the centre of the sphere circumscribing the tetrahedron is given by position vector (a^2( vec bxx vec c)+b^2( vec cxx vec a)+c^2( vec axx vec b))/(2[ vec a vec b vec c]) .

Let O be the centre of a regular hexagon A B C D E F . Find the sum of the vectors vec O A , vec O B , vec O C , vec O D , vec O Ea n d vec O F .

A B C D is a quadrilateral. E is the point of intersection of the line joining the midpoints of the opposite sides. If O is any point and vec O A+ vec O B+ vec O C+ vec O D=x vec O E ,t h e nx is equal to a. 3 b. 9 c. 7 d. 4

A B C D is a quadrilateral. E is the point of intersection of the line joining the midpoints of the opposite sides. If O is any point and vec O A+ vec O B+ vec O C+ vec O D=x vec O E ,t h e nx is equal to a. 3 b. 9 c. 7 d. 4

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 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