Which pair of angles are alternate exterior angles? A) 1 and 8
B) 1 and 7
C) 2 and 7
D) 2 and 9

Option (C)

Step-by-step explanation:

From the picture attached,

Two lines are the parallel lines and one line is intersecting these lines at two distinct points.

m∠3 = ∠6 [Alternate interior angles]

Since, angles 2 and 7 are the vertically opposite angles,

m∠2 = m∠7 [Alternate exterior angles]

Therefore, angles ∠2 and ∠7 are the pair of alternate exterior angles.

Option (C) is the answer.

sgth thdhtxr ythdsx hfgh ysrth th srtrh

step-by-step explanation:

trshd h rdhsjsdrnytjdt jyjyukfddythj

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