Aright rectangular prism has a length of 6 cm a width of 8 cm and a height of 4 cm the dimension of the prism are half what is the volume of the reduced prism

Answer 24 cm^3

Step-by-step explanation:

If the dimensions are 1/2  the volume is 1/8 the original volume. There are 2 ways to do this. I'm going to choose the most straight forward.

Formula

V = L * w * h

Givens

L = 6

w = 8

h = 4

Solution

V_original = 6 * 8 * 4 = 192

V_half = 3 * 4 * 2 = 24

V_original / V_half = 192/24 = 8/1

So the other way around (V_half/V_original) = 1/8

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