Consider the following statement s (x is a real number): vx > 10(x2> 100) a. rewrite the statement equivalently in the form vx (p(x where p is some predicate with the set of real numbers as the domain. state the general rule you are using. b. negate s formally and simplify, but do not use conjunction. c. negate the statement you found in a. and simplify. d. if you found the correct statements in b. and c., then these two statements are logically equivalent. they demonstrate a general rule about domain-restricted existential statements. state that rule.

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

c.

step-by-step explanation:

apex answer is: true.

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