Acertain university has 10 vehicles available for use by faculty and staff. four of these are vans and 6 are cars. on a particular day, only two requests for vehicles have been made. suppose that the two vehicles to be assigned are chosen in a completely random fashion from among the 10. (a) let e denote the event that the first vehicle assigned is a van. what is p(e)? 0.4 correct: your answer is correct. (b) let f denote the probability that the second vehicle assigned is a van. what is p(f | e)? incorrect: your answer is incorrect. (c) use the results of parts (a) and (b) to calculate p(e and f) (hint: use the definition of p(f |

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