6-14. Ignacio and Oliver are playing another game with the algebra tiles. After they simplify two new expressions, they are left with the expressions on their mats shown at right. They could not tell which part of the mat is greater just by looking. One way to compare the mats is to separate the and the unit tiles on different sides of the mat. Work with your team to find a way to have only on Mat A. Make sure that you are able to justify that your moves are legal. Using the same reasoning from part (a), what would you do to have only the variable on Mat B in the Expression Comparison Mat at right? Write a short note to Ignacio and Oliver explaining this new strategy. Feel free to give it a name so it is easier for them to remember.

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