Two lines, M and N, are represented by the following equations: Line M: y = x + 3
Line N: y = −2x + 6

Which of the following options shows the solution to the system of equations and explains why?

(1, 4), because the point does not lie on any axis
(1, 4), because one of the lines passes through this point
(1, 4), because both lines pass through this point
(1, 4), because the point lies between the two axes

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

0.02040816326

a variable is any characteristics, number, or quantity that can be measured or counted. a variable may also be called a data item. hope i !