1. Given that R is between A and X on a segment, draw a picture and write an equation
using the Segment Addition Postulate. Then find AR and RX if AR = 5x - 15,
RX = 3x + 1, and AX = 58.
2.
Given that R is the midpoint of segment AX, write an equation if AR = 5x - 15 and
RX = 3x + 1. Then find AR, RX, and AX.
3.
The endpoints of a segment are (-3,4) and (5, -8). Find the length of the segment to
the nearest tenth and then find the coordinates of the midpoint.

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

answer: x=3 and y=4

step-by-step explanation:

7

step-by-step explanation: