Consider the three points a = (10, −3,5), b = (0,2,4), and c = (2,1,0) in three-dimensional space.
let be the midpoint of and be the midpoint of .
a. write down the components of the three vectors ab, bc, and ca, and verify through arithmetic that
their sum is zero. also, explain why geometrically we expect this to be the case.
b. write down the components of the vector mn. show that it is parallel to the vector bc and half its
magnitude.

Nthe opening scene of the movie raiders of the lost ark, indiana jones replaces a golden statue with a bag of sand. the platform on which the statue is placed is designed to detect the mass of the statue. if the bag of sand has a different mass than the statue, then a mechanism triggers and destruction ensues. the density of gold is about 20\text{ g/cm}^320 g/cm 3 20, space, g, slash, c, m, start superscript, 3, end superscript. the density of sand can be estimated at 2.5\text{ g/cm}^32.5 g/cm 3 2, point, 5, space, g, slash, c, m, start superscript, 3, end superscript. the gold statue can be modeled as a cylinder with height 25\text{ cm}25 cm25, space, c, m and radius 8\text{ cm}8 cm8, space, c, m. in terms of \piπpi, what is the mass of sand indiana jones needs to avoid triggering the mechanism?