As part of an art installation, Larry wants to tie a piece of rope from the end of a 10m branch that is sticking out of the ground at 23.58 degrees angle to the end of a 1 m tall stake that is 4 m west of the end of the branch. The plans for the installation are shown below. Answer the questions below: 1. How many meters above the ground is the end of the branch?

2. What is the shortest possible rope length (in meters) that Larry can use to attach the end of the branch to the top of the stake? ​

the correct answer is the second option

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

because they could drop even lower..