if `vec r` is the position vector of a particle and `vec v` it's velocity then, `vec v` is?

A charge particle of mass m and charge q is projected with velocity v along y-axis at t=0. Find the velocity vector and position vector of the particle vec v (t) and vec r (t) in relation with time.

P(vec p) and Q(vec q) are the position vectors of two fixed points and R(vec r) is the position vectorvariable point. If R moves such that (vec r-vec p)xx(vec r -vec q)=0 then the locus of R is

vec a , vec b and vec c are the position vectors of points A ,B and C respectively, prove that : vec a× vec b+ vec b× vec c+ vec c× vec a is vector perpendicular to the plane of triangle A B Cdot

A particle performs SHM along a straight line and its position is vec(R ) , acceleration is vec(a) , velocity is vec(v) is and force on particle is vec(f) . Then which of the following statement are true? (i) vec(v). vec(a) is always + ve (ii) vec(v).vec(R ) may be -ve (iii) vec(f).vec(R ) is always -ve (iv) vec(v) is parallel to vec(f) sometimes

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

If the position vector of a point A is vec a + 2 vec b and vec a divides AB in the ratio 2:3 , then the position vector of B, is

If veca and vecb are position vectors of A and B respectively, then the position vector of a point C in vec(AB) produced such that vec(AC) =2015 vec(AB) 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

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

Prove that the normal to the plane containing three points whose position vectors are vec a , vec b , vec c lies in the direction vec bxx vec c+vec cxx vec a+ vec axx vec bdot