The product of two negative rational numbers is never zero always zero sometimes zero

Option 1 - The product of two negative rational numbers is never zero.

Step-by-step explanation:

To find : The product of two negative rational numbers ?

Solution :

By zero product rule,

If either a=0 or b=0 or both are zero.

i.e. the two number product will be zero if any of them is zero.

Now, this case is also valid for negative number as multiply of two negative number is positive.

As zero is not considering to be negative number.

So, the product of two negative rational numbers is never zero.

Therefore, option 1 is correct.

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