What are the similarities and differences between a tangent and a sectant?

As you know in Euclid's space (normal plane) each line or circumference can be represented a set of points.

Relative to circle a tangent is a line touching the circumference and being perpendicular to its radius at any given point on that circumference.

If circumfetence is set of points and tangent then similarly if we have set as secant .

The difference however is in the power of these intersection sets namely, because tangent is touching the circumference at only one point whereas because the secant is touching circumference at two different points.

Hope this helps.

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