Here are three displacements, each in meters: d1 = 1.5i + 1.8j - 5.0k, d2 = -1.0i + 2.0j + 3.0k, and d3 = 4.0i + 3.0j + 2.0k. what is r = d1 - d2 + d3 ((a), (b) and (c) for i, j and k components respectively)? (d) what is the angle between r and the positive z axis? (e) what is the component of d1 along the direction of d2? (f) what is the component of d1 that is perpendicular to the direction of d2 and in the plane of d1 and d2?

D1 = 1.5 i +  1.8 j  - 5.0 k

d2 = -1.0 i + 2.0 j + 3.0 k

d3 = 4.0 i + 3.0 j + 2.0k

d1 - d2 + d3

add each component separately

An  atom  (ours, not carroll's) consists of a positively charged  nucleus, surrounded by one or more negatively charged particles called  electrons. the positive charges equal the negative charges, so the atom has no overall charge; it is electrically neutral. most of an atom's mass is in its nucleus; the mass of an electron is only 1/1836 the mass of the lightest nucleus, that of hydrogen. although the nucleus is heavy, it is quite small compared with the overall size of an atom. the radius of a typical atom is around 0.1 to 0.25 nanometres (nm), whereas the radius of a nucleus is about 10-6  nm.  *  if an atom were enlarged to the size of the earth, its nucleus would be only 200 feet in diameter and could easily rest inside a small football stadium.read more on -