The sum of three numbers is 11. if you triple the second number and add the third number, the result will be equal to the first number. the first number is two times the second number. what are the numbers?
a) 1st number = 9, 2nd number = 6, 3rd number = -4
b) 1st number = 10, 2nd number = 5, 3rd number = 4
c) 1st number = 10, 2nd number = 5, 3rd number = 14
d) 1st number = 11, 2nd number = 5.5, 3rd number = -5.5

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