Answer
See explanation.
Work Step by Step
The first polarizer filters out half the incident light. At point A:
$$I_1=\frac{1}{2}I_o$$
The light at point A is polarized along the vertical direction.
The fraction filtered out by the second polarizer depends on the angle between the axes of the two polarizers, which here is 60 degrees. At point B:
$$I_2=I_1cos^2\theta=\frac{1}{2}I_o cos^2 60^{\circ}=0.125I_0 $$
At point B, the light is polarized along the axis of the second polarizer.
The fraction filtered out by the final polarizer depends on the angle between the axes of the two polarizers, which here is 30 degrees. At point C:
$$I_3=I_2cos^2\theta=0.125I_0 cos^2 30^{\circ}=0.09375I_0 $$
b. The light intensity would be zero because the first and third filters are perpendicular.
