Mrs smith wrote the following statement on the board “ a ray can be a part of a line” a group of students were discussing the meaning of the statement they were arguing back-and-forth about whether the converse (a line could be any part of a ray). of this statement is also true. billy, the group leader, determined that the converse is not true. is billy correct or not justify your answer

Billy is correct.

Step-by-step explanation:

We have that,

The converse of the given line is 'A line could be a part of a ray'.

Since, it is known that,

1. Ray - is a line segment having one end-point and other side extending infinitely.

2. Line - is a line segment having two end-points.

So, we see from the figure below that,

The ray AB has a line AC included in it.

Thus, a line can be a part of ray as we can select any point on the side extending to infinity to form a line.

Hence, Billy is correct i.e. 'A line could be a part of a ray' is true.

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