State Euclid’s Postulate 1 and Postulate 2

State Fleming.s left - hand rule.

Consider the following statement : " " There exists a pair of straight lines that are everywhere equidistant from one another. Is this statement a direct consequence of Euclid's fifth postulate ? Explain.

Use Euclid’s division lemma to show that the square of any positive integer is either of the form 3m or 3m.+ 1 for some integer m.

Use Euclid’s division lemma to show that the cube of any positive integer is of the form 9m, 9m + 1 or 9m + 8.

A 10 kg satellite circles earth once every 2 h in an orbit having a radius of 8000 km. Assuming that Bohr’s angular momentum postulate applies to satellites just as it does to an electron in the hydrogen atom, find the quantum number of the orbit of the satellite.

The electron in a hydrogen atom makes a transition n_(1) rarr n_(2) where n_(1) and n_(2) are the principal qunatum numbers of the two states. Assume the Bohr model to be valid. The frequency of orbital motion of the electron in the initial state is 1//27 of that in the final state. The possible values of n_(1) and n_(2) are

….is the scientist postulated electromagnetic waves.

Use Euclid’s division algorithm to find the gt HCF of ( 1 ) 135 and 225 ( 2 ) 196 and 382 2 0 ( 3 ) 867 and 255.