Derive the unit vector parallel to a given vector A = Axi cap + Ayj cap + Azk cap and perpendicular to A bar

Suppose you have three polarizing filters, with the second at an angle of 42∘ to the first and the third at an angle of 90∘ to the first. by what perfect will the original intensity of unpolarized light be reduced to after passing through all three filters?

How can you increase the strength of an electromagnet?

Can you match these to the correct definition