2 (k - 5) + 3k = k + 6

k=4

Step-by-step explanation:

First, distribute the 2 on the left side

2 (k - 5) + 3k = k + 6

2*k +2*-5 +3k=k+6

2k-10+3k=k+6

Combine like terms on the left side

5k-10=k+6

Add 10 on both sides

5k=k+16

Subtract k on both sides

4k=16

Divide by 4 on both sides

k=4

Hope this helps! :)

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