3. Ms. Calcutta, the owner of a business park is adding a recycling station for every three office buildings. To make it easier for the tenants, she is going to to use the circumcenter of the three office buildings to place the recycling stations. By doing this, it will be easier to get to the station, because it is equidistant from the three office buildings.

Part A; Justify the rationale behind Ms. Calcutta’s decision to use the circumcenter.

Part B: There is a garbage dumpster exactly at the midpoint of each pair of office buildings. Suppose that there are sidewalks connecting each office building to each other and to each recycling station. What is the relationship between the building-to-building sidewalk and the station-to-dumpster sidewalk?

A. All the points are equidistant toe each other.

B.  All the points are accessible and equal distance, they form right angles.

Step-by-step explanation:

A. This is a construction problem.

Let the three office buildings be the three triangle vertices. It means that on paper, all the points can be joined to give a triangle.

Next, the lines of the triangles are bisected by using perpendicular lines to them.  Joining these lines gives the midpoint of the triangle.

Hence the recycle bin is placed in the midpoint of the three office buildings.

B. The lines form right angels to the buildings. In other words, the pathways leading to the sidewalk form right angles.

10000000000000000000000000000000

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12