Determine the ratio in which the point (–6, m) divides the join of a(–3, –1) and b(–8, 9). also, find the value of m.

Ratio = 3 : 2 and value of m = 5.

Step-by-step explanation:

We are given the end points ( -3,-1 ) and ( -8,9 ) of a line and a point P = ( -6,m ) divides this line in a particular ratio.

Let us assume that it cuts the line in k : 1 ratio.

Then, the co-ordinates of P = .

But, = -6

i.e. -8k-3 = -6k-6

i.e. -2k = -3

i.e.

So, the ratio is k : 1 i.e i.e. 3 : 2.

Hence, the ratio in which P divides the line is 3 : 2.

Also, = m where

i.e. m =

i.e. m =

i.e. m =

i.e. m = 5.

Hence, the value of m is 5.

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

25.2

step-by-step explanation:

2+4x6-8/10= 25.2