If you take two steps of different sizes, can you end up at your starting point (in other words, can two vectors with different magnitudes ever add to zero)? more generally, can three or more vectors with different magnitudes ever add to zero?

a) No, Two vectors with different magnitudes can never add up to zero.

b) Yes, Three or more vectors with different magnitudes can add up to zero.

Explanation:

a) No, Two vectors with different magnitudes can never add up to zero.

Given vector A and B

A = (x1,y1,z1) and B = (x2,y2,z2)

For A + B = 0

This conditions must be satisfied.

x1 + x2 = 0

y1 + y2 = 0

z1 + z2 = 0

Therefore, for those conditions to be meet the magnitude of A must be equal to that of B.

b) Yes, Three or more vectors with different magnitudes can add up to zero.

For example, three forces acting at equilibrium like supporting the weight of a person with two different ropes.

W = T1 + T2

Where;

W = Weight

T1 = tension of wire 1

T2 = tension of wire 2

it is called kinetic energy

graph slopes whilst gas cools, then it is flat whilst conensation to liquid happens, the coolong liquid then graphs as a slope when it solidifies graph is flat

latent heat