In art class, Cassie takes a square of cardboard and weaves a wire through it, as shown in the figure. When she holds the ends of the wire, the wind spins the
cardboard on the wire axis. It this is photographed, it looks like a 3-dimensional
object. What 3-dimensional shape is generate by spinning the cardboard square on
the wire axis?

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

the thermometer is precise but not accurate

step-by-step explanation:

77

step-by-step explanation:

answer: 0,6

step-by-step explanation:

this would make it the y intercept.