En un barco, 1/7 del número de tripulantes se encarga del mantenimiento de la maquinaria, 2/7 de la cocina, 3/7 de las recámaras y pasillos, y los 18 restantes son oficiales

see the explanation

Step-by-step explanation:

The question in English is

On a ship, 1/7 of the crew members maintain the machinery, 2/7 the kitchen, 3/7 the bedrooms and corridors, and the remaining 18 are officers

Let

x ----> members that maintain the machinery

y ---->members that maintain the kitchen

z ----> members that maintain bedrooms and corridors

w ----> members that are officers

T ----> total number of members

we know that

The total sum of the fractions must be equal to 1

Remember that

The number of officers is 18

so

Find out the total number of members

solve for T

Find out the number of members that maintain the machinery

Find out the number of members that maintain the kitchen

Find out the number of members that maintain bedrooms and corridors

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