If 5 -letter words'' are formed using the letters A, B, C, D, E, F, G, how many such words are possible for each of the following conditions? a. No condition is imposed.
b. No letter can be repeated in a word.
c. Each word must begin with the letter A and letters can be repeated.
d. The letter C must be at the end and letters can be repeated.
e. The second letter must be a vowel and letters can be repeated.

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

26

step-by-step explanation:

answer: it's upside down and i can't read it

step-by-step explanation: