If and then find the dot product of ?
Here,
Find the component of vector in the direction of
We know
∴
Now component of in the direction of is,
Here,
and
Thus,
and
∴
A particle moves in XY plane, such that its position at any instant is
and
Find the angle between velocity vector and acceleration vector at any instant.
The position of the particle at any instant is,
Therefore the velocity of particle at any instant is,
Acceleration of particle at any instant is,
Now,
Since dot product of acceleration vector and velocity vector is zero, therefore the acceleration vector and velocity vector is