In order to use the pythagorean theorem to find the magnitude of a resultant vector, which must be true regarding the two initial vectors?
a)they form a 90 degree angle.
b)they are equal in magnitude.
c)they have the same directions.
d)they are parallel to one another.

The true option is a) they form a 90 degree angle.

Pythagorean theorem is valid for right triangles, which is what you can form when the two vectors have a 90 degree angle.

Regarding the other options:

b) They are equal in magnitude: this is not a condition because Pythagoream theorem is valid for any magnitude as long as the angle is 90°C.

c) They have the sam directions: false, because if the two vectors have the same directions the magnitud is the sum of the two magnitudes.

d) They are parallel: false for a similar reason that c) taking into account if they have the same direction or are opposed.  . 

         Work = (force) x (distance.

The force required to lift the load is its weight.

         Weight = (mass) x (gravity)

so    Work = (mass) x (gravity) x (distance)

Now  Power = (work) / (time)

so     Power  =  (mass) x (gravity) x (distance) / (time)

                      =  (700kg) x (9.8 m/s²) x (2 m)  /  (0.4 sec)

                      =  ( 700 x 9.8 x 2) / (0.4)  (kg-m²/sec²) / (sec)

                      =        ( 34,300 )                  (joule)  /  (sec)

                      =                     34,300 watts .

This is one of those exercises where the math and the physics
are air-tight and bullet-proof but the answer is absurd.

34,300 watts is about 46 horsepower.  I don't care how many
Wheaties Power Lifter Paul had for breakfast today, he is NOT
snatching a barbell that weighs  1,543 pounds (0.77 ton !)
to the height of the top of his head in less than 1/2 second !