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 ardius vector of point A relative to the origin varies with time t as vec(r)= at hat(j)-bt^(2) hat(j) where a and b are constants. Find the equation of point's trajectory.

A ardius vector of point A relative to the origin varies with time t as vec(r)= at hat(j)-bt^(2) hat(j) where a and b are constants. Find the equation of point's trajectory.

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.

The vector vec A varies with time as vec A=that i-sin pi that j+t^(2)hat k. Find the derivative of the vector at t=1

A particle moves in the xy plane and at time t is at the point vec r= t^(2) hat i + t^(3)-2t hat j . Then find velocity vector

Find the unit vector along vec a - vec b where veca = hat i + 3 hat j - hat k and vec b = 3 hat i + 2 hat j + hat k .

The position vector of a particle is given by vec(r ) = k cos omega hat(i) + k sin omega hat(j) = x hat(i) + yhat(j) , where k and omega are constants and t time. Find the angle between the position vector and the velocity vector. Also determine the trajectory of the particle.

(A ) Find the vector and cartesian equations of the line through the point (5,2,-4) and which is parallel to the vector 3 hat(i) + 2 hat(j) - 8 hat(k) . (b) Find the equation of a line passing through the point P(2, -1, 3) and perpendicular to the lines : vec(r) = (hat(i) + hat(j) - hat(k) ) + lambda (2 hat(i) - 2 hat(j) + hat(k)) and vec(r) = (2 hat(i) - hat(j) - 3 hat(k) ) + mu (hat(i) + 2 hat(j) + 2 hat(k)) .

For any vector vec r , prove that vec r=( vec r . hat i) hat i+( vec r . hat j) hat j+( vec r . hat k) hat kdot

For given vectors vec a = 2 hat i - hat j + 2 hat k and vec b = - hat i + hat j - hat k , find the unit vector in the direction of the vector vec a + vec b .