Suppose that n is a function of a scalar u in a reference frame r such that as u varies, n changes in such a way that it always remains perpen- dicular to a unit vector k fixed in r. let l be a line parallel to n and let ni be a unit vector parallel to a line l'fixed in r and perpendicular to k. we discussed the relation rdn/dz k x n de/dz. where e is the angle between l'and l'. show that k xn=-sinb cose ñ2 where n2 is a unit vector perpendicular to both k & nn with the sense of n2 defined in such a way that ni x i2

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 believe your answer is 99.7% of 7-year-old children are between 46.6 inches and 49.5 inches tall.