Problem

Velocity and acceleration of a particle at some instant are

\mathbf{v} = (3\hat{i} - 4\hat{j} + 2\hat{k}) \text{ m/s} \quad \text{and} \quad \mathbf{a} = (2\hat{i} + \hat{j} - 2\hat{k}) \text{ m/s}^2

(a) What is the value of dot product of

\mathbf{v}

and

\mathbf{a}

at the given instant? (b) What is the angle between

\mathbf{v}

and

\mathbf{a}

, acute, obtuse or

90^\circ

? (c) At the given instant, whether speed of the particle is increasing, decreasing or constant?