Ashipmate set aboat to sail excatly 27°ne from the dock. after traveling 120miles, the shipmate realized he had misunderstood the instructions from the captin- he was supposed to set sail going directly east! how many miles will the shipmate have to travel directly south before he is directly east of the dock?

The shipmate must travel 54.48 miles to the south

Step-by-step explanation:

We need to know how many miles south the shipmate traveled. So, we need to find the opposite side of the 27 ° angle shown in the triangle of the attached image.

To find this distance we use the following identity:

We know that the angle = 27 °.

So:

The shipmate must travel 54.48 miles to the south

answer: no

step-by-step explanation:

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