Position Vector

Show, by vector methods, that the angularbisectors of a triangle are concurrent and find an expression for the position vector of the point of concurrency in terms of the position vectors of the vertices.

The motion of a particle is defined by the position vector vec(r)=(cost)hat(i)+(sin t)hat(j) Where t is expressed in seconds. Determine the value of t for which positions vectors and velocity vector are perpendicular.

Let ABC be a triangle whose circumcenter is at P, if the positions vectors of A,B,C and P are veca,vecb,vecc and (veca + vecb+vecc)/4 respectively, then the positions vector of the orthocenter of this triangle, is:

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

A particle is projected at an angle of 30^(@)w.r.t. horizontal with speed 20m//s:( use g=10m//s^(2)) (i) Find the position vector of the particle after 1s . (ii) Find the angle between velocity vector and position vector at t=1s .

Find the vector equation of a line passing thorugh a point with position vector 2hati-2hatj+hatk and parallel to the line joining the point with the position vectors -hati+3hatj+hatk and 2hati+hatj+3hatk . Also find the Cartesian equation of this line.

A positive charge 50 muC is located in xy plane at a position vector r_0 = 4hati + 4hatj . the electric field strength E at a point whose position vector is vecr = 10hati - 4hatj is ( vecr_0 and vecr are expressed in metre)

The equation of the plane passing through three non - collinear points with positions vectors a,b,c, is