Astudent solved this problem by working backward.
tom had some marbles. he had three times as many marbles as ralph. ralph had 6 marbles. tom lost 3 marbles and bought 6 new marbles. how many marbles does tom have now?
student's solution - ralph has 6 marbles, so tom has 6 × 3 marbles to begin with. so tom has 18 marbles. he lost 3, so 18 – 3 = 15, and bought 6, so 15 + 6 = 21. so tom now has 21 marbles.
here is a problem that can also be solved by working backward.
alex bought twice as many pears as apples. he bought 4 more pears than oranges. he bought 6 apples.
how many oranges did alex buy?

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

the answer

b. they are parallel and will never intersect.