Which two numbers on the number line has an absolute value of 3? select the location of both numbers on the number line

Solution

             To    find   Which two numbers on the number line has  an

             absolute value of  3  

            Absolute   value   means    " how  far   a  number    is   from  

           zero "  .

           "3"    is    3    away   from   zero  .

           and    " -3 "   is  also   3    away   from  zero  .

           i.e

                    |  0  - 3  |   =   3

                    |  3 - 0 |  =  3

                    So ,  the  absolute   value  of   "3 "    is    3

                   similarly  , absolute  value  of  "3 "   is   3  .

                  Hence  , the  two  numbers   are   -3    and   3

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