There is three witches with a wand and a spoon which equals 45, there are three wands equals 21, there are three spoons equals 12 then there are one spoon , one witch with no wand no spoon times 7 what is the answer

73

Step-by-step explanation:

Let

a = spoon

b = wand

c = witch

Therefore;

( a + b + c ) + ( a + b + c) + ( a + b + c) = 45 equation 1

a + a + a = 21 equation 2

b + (b +b) + b = 12 equation 3

Unknown

b + ( c × ( a+a) = ? .equation 4

Solutions

From equation 1

3a = 21

a = 7

From equation 2

4b = 12

b = 3

From equation 3

( 7 + 3 + c ) + ( 7 + 3 + c ) + ( 7 + 3 + c)

= 45

10 + c + 10 + c + 10 + c = 45

30 + 3c = 45

3c = 15

c = 5

From equation 4

3 + ( 5 × (14) )

= 73

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

207/8 is the right