A force `F=Ai+Bj` is applied to a point whose radius vector relative to the origin of coordinates O is equal to `r=ai+bj`, where a, b, A, B are constants, and i,j are the unit vectors of the x and y axes. Find the moment N and the arm l of the force F relative to the point O.

A force vecF=Ahati+Bhatj is applied to a point whose radius vector relative to the origin is vecr=ahati+bhatj , where a , b , A , B are constants and hati , hatj are unit vectors along the X and Y axes. Find the torque vectau and the arm l of the force vecF relative to the point O .

A force F_1=Aj is applied to a point whose radius vector r_1=ai , while a force F_2=Bi is applied to the point whose radius vector r_2=bj . Both radius vectors are determined relative to the origin of coordinates O, i and j are the unit vectors of the x and y axes, a, b, A, B are constants. Find the arm l of the resultant force relative to the point O.

A force vecF=hat3 +4 hatj is applied to a point whose position vector is vecr=hatI +2hatj . Find the moment N and the arm l of the force F relative to the origin.

A radius vector of a point A relative to the origin varies with time t as r=ati-bt^2j , where a and b are positive constants, and I and j are the unit vectors of the x and y axes. Find: (a) the equation of the point's trajectory y(x) , plot this function, (b) the time dependence of the velocity v and acceleration w vectors, as well as of the moduli of these quantities, (c) the time dependence of the angle alpha between the vectors w and v, (d) the mean velocity vector averaged over the first t seconds of motion, and the modulus of this vector.

Find the potential varphi (x,y) of an electrostatic field E = 2axyi + a (x^(4) - y^(2)) j , where a is a constant, I and J are the unit vectors of the x and y axes.

A radius vector of point A relative to the origin varies with time t as vec r = at hat i - bt^2 hat j where a and b are constant. The equation of point's trajectory is.

A radius vector of point A relative to the origin varies with time t as vec r = at hat i - bt^2 hat j where a and b are constant. The equation of point's trajectory is.

The electric field strength depends only on the x and y coordinates according to the law E = a (x i + yj) (x^(2) + y^(2)) , where a is a constant , i and j are the unit vectors of the x and y axes. Find the flux of the vector E through a sphere of raidus R with its centre at the origin of coordinates.

There are two stationary fields of force F=ayiand F=axi+byj, where i and j are the unit vectors of the x and y axes, and a and b are constants. Find out whether these fields are potential.