I got the measurements but i dont know how to put it in a sentence that makes sense A rectangle with vertices J(2, 0) K(0,0) L(0,8) and M(2, 8) is rotated around the y-axis.

A. Use complete sentences to describe the resulting solid. Include the specific measurements for the solid’s dimensions such as height, width, length, radius, etc.

B. To the nearest tenth of a cubic unit, what is the volume of the resulting three-dimensional figure? Include all of your calculations.

after graphing the points, describe the shape, (ex, rectangle) then mesure the points of the width, hight, or any other things. then multiply the length and the heaght and the thickness to get b

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