This is algebra and I don't understand

To understand this, bags of gas added make it go up, while bags of sand added make it go down:

1). Add bags of gas | balloon goes UP | 3 bags of gas ( +3 ), 10 bags of sand ( +10 )

2). Add bags of sand | balloon goes DOWN | 3 bags of sand ( -3 ), 10 bags of sand ( -10 )

3). Subtract bags of gas | balloon goes DOWN | subtract 3 bags of gas - ( +3 ), subtract 10 bags of gas - ( +10 )

4). Subtract bags of sand | balloon goes UP | subtract 3 bags of sand - ( -3 ), subtract 10 bags of sand - ( 10 )

the answer is b

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