Triangle ABC has vertices A(0, 4), B(2, 1), and C(4, 3). Find the

Let: u, v, w \varepsilon R3<br><br> Prove: (u x v) * [(v x w) x (w x u)] = [u * (v x w)]2

sweet [91]

Recall that for 3 vectors $a,b,c$ , all in $\mathbb R^3$ , the vector triple product

$a\times(b\times c)=(a\cdot c)b-(a\cdot b)c$

So

$(v\times w)\times(w\times u)=((v\times w)\cdot u)w-((v\times w)\cdot w)u$

Also recall the scalar triple product,

$a\cdot(b\times c)$

which gives the signed volume of the parallelipiped generated by the three vectors $a,b,c$ . When either $a=b$ or $a=c$ , the parallelipepid is degenerate and has 0 volume, so

$(v\times w)\cdot w=0$

and the above reduces to

$(v\times w)\times(w\times u)=((v\times w)\cdot u)w$

so that

$(u\times v)\cdot[(v\times w)\times(w\times u)]=(u\times v)\cdot((v\times w)\cdot u)w$

The scalar triple product has the following property:

$a\cdot(b\times c)=b\cdot(c\times a)=c\cdot(a\times b)$

Since $(v\times w)\cdot u$ is a scalar, we can factor it out to get

$((v\times w)\cdot u)((u\times v)\cdot w)$

and by the property above we have

$(u\times v)\cdot w=u\cdot(v\times w)$

and so we end up with

$[u\cdot(v\times w)]^2$

as required.

4 0

3 years ago

Compare the given dimensions of four triangles. Which triangle is possible to construct?

Mila [183]

Answer:

I can't see the triangles give me the coordinates

Step-by-step explanation:

8 0

2 years ago

Combine like terms to create an equivalent expression -4/7p+(-2/7p)+1/7

STatiana [176]

-6/7p+1/7 um Idk what you wanted me to do but I added -4/7p with -2/7p

7 0

3 years ago

Read 2 more answers

Screenshoted question below

kumpel [21]

Answer:

y=x+4

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

The equation c = 35h + 60 describes a plumber's charges, c, for a job that takes h hours. Which statement is correct?

VikaD [51]

The complete question is

"The equation c = 35h + 60 describes a plumber's charges, c, for a job that takes h hours. Which statement is correct?

a. The domain of this function represents the total cost for a job

b. H is a function of C

c. The painter charges a $35 service fee in addition to an hourly rate

d. The painters hourly rate is $35.00"

The equation c = 35h + 60 describes a plumber's charges, c, for a job that takes h hours. So, the correct option is D. The painters hourly rate is $35.00

<h3>What is a function?</h3>

Function is a type of relation, or rule, that maps one input to specific single output.

The equation c = 35h + 60 describes a plumber's charges, c, for a job that takes h hours.

The fixed fee, or service fee, is $60.

$35 is the hourly fee since in the function, it is 35 that is multiplied by the number of hours.

So, the correct option is D. The painters hourly rate is $35.00

Learn more about function here:

brainly.com/question/2253924

#SPJ1

4 0

1 year ago