What is the length of segment FG? A. 3.16
B. 15.20
C. 4.58
D. 10.49

Please help me with this

D. 10.49

Step-by-step explanation:

(see attached for reference)

Here we have two right triangles formed by dividing a larger right triangle by the Altitude (height) of the larger right triangle.

In this special case, all 3 triangles (2 small and 1 large) are SIMILAR and hence we can use the ratios of similar triangles to solve this.

In our case, ΔGFE is similar to ΔGHF

hence FG/GE = GH/FG

We are given that GE = 10 and GH = 11, hence

FG/10 = 11/FG

FG² = (10)(11)

FG² = 110

FG = ±√110

FG= 10.49

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

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