Find the equation of the line through the points (-2,-9) and (5,12)
y =

y - 12 = 3(x - 5)

Step-by-step explanation:

Going from (-2, -9) to (5, 12), x (the run) increases by 7 and y (the rise) increases by 21.  Thus, the slope of this line is m = rise / run = 21/7 = 3.

Using the point-slope formula y - k = m(x - h), we get:

y - 12 = 3(x - 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