In triangle abc, m∠acb = 42°. the angle bisectors ad and be intersect at point o so that ae + oe = ab. find m∠a and m∠b.

∠ABC = 84°

∠CAB = 54°

Step-by-step explanation:

Assume that a point on side AB, its point F

so that,  EA = FA

Then triangle AEO ≅  triangle AFO

So,

OF = OE = BF

Triangle BOF  is isosceles.

∠CEO=180−∠ABC

So that,

180 − ∠ABC + 42 = 180

Now solve for ∠ABC.

∠ABC = 84°

∠CAB = 180 - 84 - 42 = 54°

That's the final answer.

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