The torque $\overrightarrow{z}$ on a body about a given point is found to be $\overrightarrow{A} \times \overrightarrow{L}$ where $\overrightarrow {A}$ is a constant vector and $\overrightarrow{L}$ is angular momentum about that point . From this it follows that. 1) $\large\frac{dL}{dt}$ is perpendicular to $\overrightarrow {L}$ at all times 2) the component of $\overrightarrow {L}$ in the direction of $\overrightarrow{A}$ does not change with time. 3) the magnitude of $\overrightarrow {L}$ does not change with time. 4) $\overrightarrow {L}$ does not change with time. Which of the following is correct?

Question

a) 1,2 and 3

b) 2,3 and 4

c) 1,3 and 4

d) 1,2 and 4