5

(1 point) Find the distance the point P(-1, -5, 1), is to the plane through the three points Q(-3, 22, 4) , R(, 6,-7) , and S(O, 3, 0)....

Question

(1 point) Find the distance the point P(-1, -5, 1), is to the plane through the three points Q(-3, 22, 4) , R(, 6,-7) , and S(O, 3, 0).

(1 point) Find the distance the point P(-1, -5, 1), is to the plane through the three points Q(-3, 22, 4) , R(, 6,-7) , and S(O, 3, 0).



Answers

Find the distance between the point and the plane. $$\begin{aligned} &(1,3,-1)\\ &3 x-4 y+5 z=6 \end{aligned}$$

Okay, So we asked upon the distance from the points P one comma two, comma three neglect you and the equation. It was an X minus three. But to why was one is equal to r minus. Worthing, you don't thing. So we can actually write equations to this. Exposed to wind my fourth e minus one itself. Okay, you see that Are normal. Back through for our plane is in physical, too. 1234 s. So we know that the points Q, which is one comma zero company Roland lives on our plane. So our component form of the vector from cute to be nickel to one when it's one college, two minutes. Zero come in three minutes. Did you get that secret to Joe? Come on, Number two, number three. No, it's fine. This thief on the plane to appoint me So we have d is equal to projection of u P on to end. But it's the same man the camp of Q P on to end magnitude, u p times and overtime. I do, Ben, That gives me You're 16 over Scarlett's 21

Hello. So here the distance from the point to one negative one. Um From the plane here x minus two Y plus two Z plus five equals zero. That is going to be given by the absolute value of two minus two um Times one plus two times negative one plus five. All divided by the square root of one squared plus two Squared plus two squared an absolute value. So this here is going to be equal with the top. This just becomes equals to 3/3. So this is what we evaluate this. This is equal to 3/3 which is equal to one. So here the distance is just equal to one unit.

For this problem, we want to find the distance from the point to the plane. So we know the point and we know the plane. So now we just need to do the calculations. We know that the distance is going to be equal to and peanut dot p over magnitude of an so based on what we have here we have three, There's gonna be three times 1 Because three comes from the plane and one comes from the point. It has to be plus two times negative, two plus six times four And then we have -5 because that's the constant term, that's all divided by the magnitude of n. Where an is 3- six, the normal vector. So the magnitude van is going to be the square root of three squared plus two squared plus six squared. That ends up giving us 18 over route 49, Which is 18/7. Final answer.

For this problem. We know the point one negative. 24 we know three X plus two I plus six z equals five. And we know our distance is going to be equal to the amplitude or the magnitude of end dot peanut dot p all over the magnitude of n. So when we do our calculations, um, the question gives us everything we need to plug in our formula. Um, so we're going to use an our normal vector, but we have to rise that and is going to equal 3 to 6 based on the equation of the plane that were given. So our distance is going to be equal to 18. Over the magnitude of end is Route 49. So that's the same thing as 18/7. And that is going to be our final answer for the distance between that line or that point and the plane


Similar Solved Questions

5 answers
Let the trigonometric function bc defined os f6-) Zcos (3*}.what . the amolitude? What the period? Skctch Pcriod of f
Let the trigonometric function bc defined os f6-) Zcos (3*}. what . the amolitude? What the period? Skctch Pcriod of f...
5 answers
Tha ~sanse of rotation of the rod AB will be
Tha ~sanse of rotation of the rod AB will be...
5 answers
Question 2The direction of the net force on charge -qis+QLeftRightThe orce= "qiszero.Dwn
Question 2 The direction of the net force on charge -qis +Q Left Right The orce= "qiszero. Dwn...
5 answers
21) Which of the following reactions will produce the given product in good yield? Select all that applyNuBracetonaOso_CH;NaBr acetoneOSo_Ch;EOHMeQHOSo_Ch;McONa MoOHOHMGONu MoOH
21) Which of the following reactions will produce the given product in good yield? Select all that apply NuBr acetona Oso_CH; NaBr acetone OSo_Ch; EOHMeQH OSo_Ch; McONa MoOH OH MGONu MoOH...
5 answers
Which of the following is the correct graph of mass (m) versus For the simple pendulum; period (t)? mssSelect one: 0)c) ^) 8)
Which of the following is the correct graph of mass (m) versus For the simple pendulum; period (t)? mss Select one: 0) c) ^) 8)...
5 answers
'1COSI(6) lim T4++04 1 B. 4 C. 0'a HEDO"J #tooF dloes not exist] ( nut #hunicquelimit )Hanswer;
'1 COSI (6) lim T4++0 4 1 B. 4 C. 0 'a HEDO "J #too F dloes not exist] ( nut #hunicquelimit ) Hanswer;...
5 answers
The Ksp calcium hydroxide. 20 | Ca(OH)z. 5.02 3 Calculate the solubility of this compound in grams#boutus 1privacy policy 1
The Ksp calcium hydroxide. 20 | Ca(OH)z. 5.02 3 Calculate the solubility of this compound in grams #boutus 1 privacy policy 1...
5 answers
(1 point) Solve the initial value problemdy _ y= 8e" + 30e6r dxwith y(o) 10.helfy
(1 point) Solve the initial value problem dy _ y= 8e" + 30e6r dx with y(o) 10. helf y...
5 answers
(Z0 pl-} Lul :R' _Bbe delized Dy sctLiugil (t,") (0,0) ("") A (,0)flt.w)Show that % (0,01 and 3(0,0) exist (Q0 (b) Find @(j,V) Atdl @(r,w) lr (r,w) (U.O): (2) Show ix ol clust Cl ou R?. Vliaut: SLow tull "(.W) puduct & boutelerl Iuuctiuu nl G(r,v) eqjunla Ule prexluct of = Mc [ Innuulecd fut ticu.] (a) Show" thnr both 240,0) and 31.0,0} exlt (D,W) bult nro not rm Flcta
(Z0 pl-} Lul :R' _Bbe delized Dy sctLiug il (t,") (0,0) ("") A (,0) flt.w) Show that % (0,01 and 3(0,0) exist (Q0 (b) Find @(j,V) Atdl @(r,w) lr (r,w) (U.O): (2) Show ix ol clust Cl ou R?. Vliaut: SLow tull "(.W) puduct & boutelerl Iuuctiuu nl G(r,v) eqjunla Ule prexluct...
5 answers
Chlorophyceae are grass green due to the dominance of pigment(a) Chlorophyll $mathrm{a}, mathrm{c}$(b) Chlorophyll $mathrm{b}, mathrm{a}$(c) Chlorophyll d, c(d) All of these
Chlorophyceae are grass green due to the dominance of pigment (a) Chlorophyll $mathrm{a}, mathrm{c}$ (b) Chlorophyll $mathrm{b}, mathrm{a}$ (c) Chlorophyll d, c (d) All of these...
1 answers
Exercises $9-10:$ Use the method of least squares to express $y$ as a linear function of $x$ $$\begin{array}{c|c|c|c|c|c|c} x & 40 & 42 & 43 & 44 & 46 & 49 \\ \hline y & 15 & 18 & 20 & 24 & 28 & 33 \end{array}$$
Exercises $9-10:$ Use the method of least squares to express $y$ as a linear function of $x$ $$\begin{array}{c|c|c|c|c|c|c} x & 40 & 42 & 43 & 44 & 46 & 49 \\ \hline y & 15 & 18 & 20 & 24 & 28 & 33 \end{array}$$...
5 answers
The proper sequence for the standard parts of letter isSelect one: Heading; date_ inside address, salutation, body, complimentary close_ signature block.Inside address, heading, date, salutation, body; complimentary close, typewritten name Salutation, date_ heading, inside address_ body, complimentary close_ signature block. Date, heading, inside address, salutation, body; typewritten name_ complimentary close
The proper sequence for the standard parts of letter is Select one: Heading; date_ inside address, salutation, body, complimentary close_ signature block. Inside address, heading, date, salutation, body; complimentary close, typewritten name Salutation, date_ heading, inside address_ body, complimen...
5 answers
Generally speaking, as p-values get lower, the associatedt-statistics ___. A. decrease B. increase C. get closer to zero D.get farther from zero
Generally speaking, as p-values get lower, the associated t-statistics ___. A. decrease B. increase C. get closer to zero D. get farther from zero...
5 answers
Question 20/ 5Vtem Rolic is Clenettenn PrartonAnuckdevee brcIdc"ldut s hclueucy 0l 22.537M+? withace (lliten ; buriratlo Dotetming tte Wwlenethol tno cxemmnaceuktalcilnaUieu Ul 29079 -10 "uuetolrnl HdeltYcur Jnvc enlle encuct
Question 20/ 5 Vtem Rolic is Clenettenn Prarton Anuckdevee brcIdc"ldut s hclueucy 0l 22.537M+? withace (lliten ; buriratlo Dotetming tte Wwlenethol tno cxemmnaceuktalcilnaUieu Ul 29079 -10 "uuetolrnl HdeltYcur Jnvc enlle encuct...
5 answers
[References]Give the number of significant figures in the following numbers(a) 0.00546(6) 1600(c) 2.300E-4(d) 2.34E+9Submit AnswerTry Anothor VerslonItem attempts remainingLpt1pi1pr1pt
[References] Give the number of significant figures in the following numbers (a) 0.00546 (6) 1600 (c) 2.300E-4 (d) 2.34E+9 Submit Answer Try Anothor Verslon Item attempts remaining Lpt 1pi 1pr 1pt...
5 answers
2. The base ofa solid is the region enclosed by the graph ofy = 3(x ~ 2)2 and the coordinate axes If every cross section perpendicular to the X-axis is square, then the volume ofthe solid is a: 8.0 b. 19.2 24.0 25.6 57.6
2. The base ofa solid is the region enclosed by the graph ofy = 3(x ~ 2)2 and the coordinate axes If every cross section perpendicular to the X-axis is square, then the volume ofthe solid is a: 8.0 b. 19.2 24.0 25.6 57.6...
5 answers
Calculate AG? (kJlmole) at 298 K for the reaction below:HzS04() = HzO(l)+ SOa(g)K-2.07x10-12Enter a number to 2 decimal places_
Calculate AG? (kJlmole) at 298 K for the reaction below: HzS04() = HzO(l)+ SOa(g) K-2.07x10-12 Enter a number to 2 decimal places_...

-- 0.065628--