Rosalie and Tom are creating patterns.

Rosalie uses the rule “add 4” and starts at 3.
Tom uses the rule “add 8” and starts at 7.

Which best compares Rosalie's and Tom's patterns?

A. Tom's number is always equal to Rosalie's number plus 4.

B. Tom's number is always twice as large as Rosalie's number.

C. Tom's number minus Rosalie's number is always divisible by 4.

D. Tom's number is always 3/2 times larger than Rosalie's number.

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

false

step-by-step explanation: