Et A = (2, 4), B = (4, 5), and C = (6, 1). Draw three new triangles as follows: PQR has P = (11, 1), Q = (10, -1), and R = (6, 1);
∆ KLM has K = (8, 10), L = (7, 8), and M = (11, 6);
∆ TUV has T = (-2, 6), U = (0, 5), and V = (2, 9).
These triangles are not obtained from ABC by applying a vector translation. Instead, each of the appropriate transformations is described by one of the suggestive names reflection, rotation, or glide-reflection. Decide which is which and explain your answers.

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

what

step-by-step explanation: