Which property of addition is shown below?

a + bi + c + di = a + c + bi + di

identity property
associative property
commutative property
inverse property

well, since the commutative property states that no matter how the numbers are arranged, the outcome is still going to be the same, i would say that this is demonstrating the commutative property. correct?

Consider the given expression:

a+bi+c+di = a+c+bi+di

We have to identify the property of addition in the above expression.

Since, we can observe here that (bi+c) is expressed as (c+bi).

Commutative property of addition states that the numbers can be added in any of the order. Mathematically, it states that a+b = b+a.

Here, (bi+c) is replaced by (c+bi), whether 'b' is added to 'ci' or 'ci' is added to 'b', the result is always same.

Therefore, commutative property of addition is the correct answer.

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