Which scenario will drain the battery in the circuit diagram fastest: three 20 W bulbs in positions one, two, and three or 80 W bulbs at positions 1 and 3 with a gap at position two? How do you know?

The first scenario will drain the battery faster.

Explanation:

The first scenario, since the three bulbs would be connected in series, there is no interruption in the circuit and the current can flow freely around the circuit. While in the second scenario there is an open gap, where the passage of the current is interrupted and therefore bulbs located in spaces 1 and 3 would not work.

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west