5

(W1. We) be vectors in the plane and let (5 points) Let & - (u1. U2} &nd nuinber: Prove that c(u . U) (ci)real...

Question

(W1. We) be vectors in the plane and let (5 points) Let & - (u1. U2} &nd nuinber: Prove that c(u . U) (ci)real

(W1. We) be vectors in the plane and let (5 points) Let & - (u1. U2} &nd nuinber: Prove that c(u . U) (ci) real



Answers

Prove that if $\mathbf{u}, \mathbf{v},$ and $\mathbf{w}$ are vectors in $R^{3},$ no two of which are collinear, then $\mathbf{u} \times(\mathbf{v} \times \mathbf{w})$ lies in the plane determined by $\mathbf{v}$ and w.

In this problem, we're going to use the concept of cross products in order to determine in which plane a certain victor lights. Now, the first victor is given to be the victor. You cross. We cross W. Now we need to prove that this lies in the plane determined by V and W. Now for that we need to understand that V cross W is uh victor which lies in the plane, which is normal to both V. And that means that we cross W lies in the plane, which is normal to the plane determined by the N. W. Then you cross a cross W means that this vector will be normal to both you, and it will also be normal to V. Cross W. So that means that this victor is normal to a vector which is already normal to the plane, which is determined by V. N. W. So that means that this victor will lie in the plane determined by VM W. And thus are proof is completed. Similarly, the 2nd Victor is you grass v across W. And we need to prove that the slides on the plane determined by U. And V. So for that you need to understand that you cross V. Is a victor which is normal to both U and V. So it is a victor which is normal to the plane determined by U. And V. This entire vector U crossed V. Cross W will thus be a victor which is normal to W. And is also normal to you cross W. Since you cross V. So since this victor is normal to you cross V. That means it is normal to a victor which is normal to the plane determined by you envy. So that means that this victor you cross. We crossed W. Lies in the plane determined by you envy. And thus are proof is complete.

You hear the V and W ever seen our fight so we can promise eyes be as x one x two x three Explore and exploit and also for taboo We can also writes why one what two was three wife for in a wife I So for the left since I So it is our in the V plus w So that is you come to our score x one x two Ex trio exploring and ex Fine. So plus why Won't want to What's really what for? In a white car? So here the ico to are in the x plus x one y one x two plus white too inter explain because we're for in for the right hand side. So it is a culture V plus W In this occurred, you are x one or X two into our expired. And there's a c culture are why one? Ah, why too or the way to our WiFi. So if you add them together, yours gets our injure x one plus what I want and for the way to our expired Sansa WiFi so you can find so these factor into this matter the art Deco So we can conclude that, uh, times the cost abou it because your RV plus our top here

So in order to prove this this equation over here, we would have to Well, it's just work through it. So we have our vector you as all its components you want in you too. Same thing goes for V, so it's funded are parked. To do that, we will multiply our ex components so you won. And then everyone. And then we will add them to the product of our Why components you to envy too? Great. We have found you dot fee. Now let's find v dot You You did this in blue. So vida part do, he would take the product of the I components. So v one both played by you want and we'll add them to our why component or R j component. So we have you or V two times YouTube. Now this this equation or this expression would look quite familiar. Yes, it is the same thing as the part of the fun before just in different orders. Well, as you know, this is correct. Ist for example, two times three is equal to three times to the match is not matter or the order does not matter. When you were both playing So since these two are the exact same, we have ah, have a V one here. The one here. You have a you won and the U one and we will have a V two. Me too. You to you too. Since these two are seem Yeah, just verified this equation.

Yes. So here we're grains. Approve R plus s b sico two R b class s me So you know problems the sing off I so we can ride to be as x one x two Ex tree x for an X five teeth is a fine time mission after injure plus X tom V is equal to r plus s times x one x two x three Explore and explained So this were echoed to our past This x want in their r plus s Next to in the r plus is ex tree in there are pluses Thanks for Plus is exploit So this is ah, left home. Hence I and for the right hand side So we know that Artis plus if RV plus SB is coach to our x one x two x three explore and exploit cause if x one x two x three x four and expired. So there you go to our ex one r X to our ex tree are explorers and our X by the U plus. Yes, X one is X two s ex tree is explored in the expired. So actually this is you could too. R plus is excellent in the closest it's too in the Hamptons is extreme in the r plus s x four in r plus s explain And so so here they are Ekho. So we know that our Times X Maybe it's the culture RV cost SP.


Similar Solved Questions

5 answers
An extended body (not shown in the ~fgurethe has its center of mass (CM) at the origin of the reference frame In the case below give the direction for the torgue with respect to the CM on body due to force F acting on the body at location indicated by the vectorTorque the vector product of and F_ Use the right hand rule to determine the direction of the torque_ Slbmit Answer Incrrcec Tries 2/3 Previous Tries
An extended body (not shown in the ~fgurethe has its center of mass (CM) at the origin of the reference frame In the case below give the direction for the torgue with respect to the CM on body due to force F acting on the body at location indicated by the vector Torque the vector product of and F_ U...
5 answers
12. (10 pts) Find the general solution of the differential = equatior below. y' - 2+2
12. (10 pts) Find the general solution of the differential = equatior below. y' - 2+2...
5 answers
For sample of nine automobiles; the mileage (in ODOs of miles) at which the original front brake pads wcrc worn to I0%c of their original thickness was measured, was the mileage which the original rear brake pads wene worn 105 of their original thickness_ The results are given in the following tableAutomobile Front Kear32.8 41.2 26.6 35.2 36.6 46.1 36.4 46.0 29.2 39.9 40.9 51.7 40.9 51.6 46.1 36.6 473
For sample of nine automobiles; the mileage (in ODOs of miles) at which the original front brake pads wcrc worn to I0%c of their original thickness was measured, was the mileage which the original rear brake pads wene worn 105 of their original thickness_ The results are given in the following table...
5 answers
(6ldi)46.1.529 JIjuJi?Calculate As? (J/K) for the reaction(SiCla (g) + 2Mg (s) 2MgCl2 (s) + Si (sSubstance: (Mgts)SiCl4 (g) MgCl2(s) SitsS?(J/K-mol): 330.73 32.68 89.62 18.83254.96+254.96 -198.02 -198.02+
(6ldi)46.1.5 29 JIjuJi ?Calculate As? (J/K) for the reaction (SiCla (g) + 2Mg (s) 2MgCl2 (s) + Si (s Substance: (Mgts) SiCl4 (g) MgCl2(s) Sits S?(J/K-mol): 330.73 32.68 89.62 18.83 254.96+ 254.96 - 198.02 - 198.02+...
5 answers
QUESTion 16Four different catalysts (CI, C2.C3.and C4) can be used to increase the yield of a chemical reaction To compare the effectiveness of the catalysts. statistician has collected the 3-replicate data given below: estimate the treatment effect of C2.100
QUESTion 16 Four different catalysts (CI, C2.C3.and C4) can be used to increase the yield of a chemical reaction To compare the effectiveness of the catalysts. statistician has collected the 3-replicate data given below: estimate the treatment effect of C2. 100...
5 answers
Evaluate: Use reduced fractions instead of decimals in your answer:[dt+c
Evaluate: Use reduced fractions instead of decimals in your answer: [ dt +c...
5 answers
Question (4 Points)Q-usinga 3 point ( second order) interpolatingpolynomial,the valueatx-1.3 is (Use 4 digits )Fl) 3320 8.166 15.780 59.151.75 23 34Enter your answer
Question (4 Points) Q-usinga 3 point ( second order) interpolatingpolynomial,the valueatx-1.3 is (Use 4 digits ) Fl) 3320 8.166 15.780 59.15 1.75 23 34 Enter your answer...
5 answers
Find the integer p, If Nul A is a subspace of RP, and the matrix A is as follows: 3 ~1 9 -2 A= 2 -5 5 ~2 60 a 20 b 30 c Cannot be determined0 d 4
Find the integer p, If Nul A is a subspace of RP, and the matrix A is as follows: 3 ~1 9 -2 A= 2 -5 5 ~2 6 0 a 2 0 b 3 0 c Cannot be determined 0 d 4...
1 answers
While working on a high-rise building, a construction worker drops a bolt from $320 \mathrm{m}$ above the ground. After $t$ seconds, the bolt has fallen a distance of $s$ metres, where $s(t)=5 t^{2}, 0 \leq t \leq 8 .$ The function that gives the height of the bolt above ground at time $t$ is $R(t)=320-5 t^{2} .$ Use this function to determine the velocity of the bolt at $t=2$.
While working on a high-rise building, a construction worker drops a bolt from $320 \mathrm{m}$ above the ground. After $t$ seconds, the bolt has fallen a distance of $s$ metres, where $s(t)=5 t^{2}, 0 \leq t \leq 8 .$ The function that gives the height of the bolt above ground at time $t$ is $R(t)=...
5 answers
3. Question on systematic samplinga) If ρ is close to 0, it was said that the outcome using simplerandom sampling is equivalentto the outcome using systematic sampling in term of accuracy ofestimation. Why is it so?b) If ρ is close to 1, it was said that the outcome using simplerandom sampling is better thanthe outcome using systematic sampling in term accuracy ofestimation. Why is it so?
3. Question on systematic sampling a) If ρ is close to 0, it was said that the outcome using simple random sampling is equivalent to the outcome using systematic sampling in term of accuracy of estimation. Why is it so? b) If ρ is close to 1, it was said that the outcome using simple random sa...
5 answers
EIQ -1.66 +0.07 +0.14 +0.77AP++3e" + Al(s) AgBr(s) + e + Ag(s) + Br Sn"+ + 2e" - Sn + Fe-+er - Fez+Consider the following standard reduction potentials in acid solution: The strongest reducing agent among those shown above is|Fe^+3Fe +24l+3
EIQ -1.66 +0.07 +0.14 +0.77 AP++3e" + Al(s) AgBr(s) + e + Ag(s) + Br Sn"+ + 2e" - Sn + Fe-+er - Fez+ Consider the following standard reduction potentials in acid solution: The strongest reducing agent among those shown above is| Fe^+3 Fe +2 4l+3...
5 answers
Calculate AS for heating one mole of liquid water from 20 to 100 %C at atm pressure: The molar heat capacity at constant pressure is 75.3 JKmola. 121.2b. 19.8 J/Kmol15.8 J/Kmold. 18.17 J/Kmol95.2 J/Kmol
Calculate AS for heating one mole of liquid water from 20 to 100 %C at atm pressure: The molar heat capacity at constant pressure is 75.3 JKmol a. 121.2 b. 19.8 J/Kmol 15.8 J/Kmol d. 18.17 J/Kmol 95.2 J/Kmol...
5 answers
Prove by induction that 1 . 2 + 2 . 3 + 3 4 ++"n_4utl) for n=2,3_1)n
Prove by induction that 1 . 2 + 2 . 3 + 3 4 ++ "n_4utl) for n=2,3_ 1)n...
5 answers
In a raffle, 1% of tickets are gold tickets and 8% are silver tickets_ Gold tickets are worth S15 and silver tickets are worth S10_If tickets cost S2 and you purchase single ticket, what is your expected profit?
In a raffle, 1% of tickets are gold tickets and 8% are silver tickets_ Gold tickets are worth S15 and silver tickets are worth S10_ If tickets cost S2 and you purchase single ticket, what is your expected profit?...
5 answers
Exercise 10.7. Find the local maximum and minimum values and saddle point of f(w,y) = e3y(y - 14) .
Exercise 10.7. Find the local maximum and minimum values and saddle point of f(w,y) = e3y(y - 14) ....
5 answers
0/1 Points]DETAILSPREVIOUS ANSWERSSCALCET9 4.7.008_whose perimeter is as small as possible_ (Enter the dimensions 35 comma separated list:) Find the dimensions of a rectangle (in m) with area 1,331 m
0/1 Points] DETAILS PREVIOUS ANSWERS SCALCET9 4.7.008_ whose perimeter is as small as possible_ (Enter the dimensions 35 comma separated list:) Find the dimensions of a rectangle (in m) with area 1,331 m...

-- 0.024070--