" at which velocity vector is at an angle of "(pi)/(4)

A point moves in the plane xy according to the law x=at , y=at(1-alphat) , where a and alpha are positive constants, and t is time. Find: (a) the equation of the point's trajectory y(x) , plot this function, (b) the velocity v and the acceleration w of the point as functions of time, (c) the moment t_0 at which the velocity vector forms an angle pi//4 with the acceleration vector.

A point moves in xy-plane according to equation x = at, y = at (l - bt) where a and b are positive constants and t is time. The instant at which velocity vector is at pi//4 with acceleration vector is given by:

If vec b is a unit vector in xy- plane making an angle of (pi)/(4) with the x -axis,then vec b is equal to

If veca is unit vector in xy-plane making an angle (pi)/(4) with the x-axis, then veca is equal to -

A unit vector in the xy-plane that makes an angle of pi/4 with the vector hati+hatj and an angle of 'pi/3' with the vector 3hati-4hatj is

A point moves according to the law" "x= at, y=at (1 -alphat) where a and alpha are positive constants and t is time . If the moment at which angle between velocity vecotrs and acceleration vectors is (pi)/(4) is given by (A)/(alpha) . Find the value of A .

Find a unit vector in XY plane which makes an angle 45^(@) with the vector hati + hatj at angle of 60^(@) with the vector 3 hati - 4 hatj.