Find the LCM of 42,63 and 84

 252

Step-by-step explanation:

LCM is Least Common Multiple

You can do this the long way (by find the multiples of each and seeing which one they have in common):

Multiples of 42: 42, 84, 126, 168, 210, 252

Multiples of 63: 63, 126, 189, 252

Multiples of 84: 84, 168, 252

The first multiple they have in common is 252

or

You can do this by finding their prime factorization, identifying what they have in common, and multiplying the "left overs".

Prime factorization of 42: 2 · 3 · 7

Prime factorization of 63: 3 · 3 · 7

Prime factorization of 84: 2 · 2 · 3 · 7

Common factors (common to at least two of the terms) are: 2 · 3 · 7 = 42

Left overs (see bolded numbers above) are: 2 · 3 = 6

Common terms x left overs = LCM: 42 x 6 = 252

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

i think the answer is b