5

5. Projections Scalur Yw jctimanjceth 4 6 S(eler UvtUmp a6a6 . ces 04 4'6 Fnn Th m / Lnp &E.fi (es 0 141Vectwr Pwjectitn_ 4 1 mhi . (corPa 6 ) prj_ Iai nth...

Question

5. Projections Scalur Yw jctimanjceth 4 6 S(eler UvtUmp a6a6 . ces 04 4'6 Fnn Th m / Lnp &E.fi (es 0 141Vectwr Pwjectitn_ 4 1 mhi . (corPa 6 ) prj_ Iai nthl U"j' Oat ntr 4 &Example 3; Find the scalar and vector projections ofb ontoaifa = <1,4> andb= <2,37.r;6 =41(19> = <8'% )Gomp

5. Projections Scalur Yw jctim anjceth 4 6 S(eler Uvt Ump a6 a6 . ces 0 4 4' 6 Fnn Th m / Lnp & E.fi (es 0 141 Vectwr Pwjectitn_ 4 1 mh i . (corPa 6 ) prj_ Iai nthl U"j' Oat ntr 4 & Example 3; Find the scalar and vector projections ofb ontoaifa = <1,4> andb= <2,37. r; 6 = 41(19> = <8'% ) Gomp



Answers

The projections of a vector on the three coordinate axis are $6,-3,2$ respectively. The direction cosines of the vector are (A) $6,-3,2$ (B) $\frac{6}{5},-\frac{3}{5}, \frac{2}{5}$ (C) $\frac{6}{7},-\frac{3}{7}, \frac{2}{7}$ (D) $-\frac{6}{7},-\frac{3}{7}, \frac{2}{7}$

In problem 99. The projections of victor on the three coordinate axes are 6 -3 and two. We want to find the direction designs of this, we can express a victory. For example, a that equals The magnitude of eight. Multiplied by the projection of a. And toy six multiplied by I plus the projection of The victor in two G blow by J plus the projection of the victor on that access or key or to blow your bike plus talking. Then we can't find the direction cuisines but a little correction here. This is not a this is a vector in the direction of a because this is not an object. And to get a unit vector in the direction of a. You can say that he had, we just divide by the magnitude of a then just a correction. This is not a You can say that it's w where W is in the direction of can find W head that equals the same direction six I minus three G plus two. K. Want to play it by the magnitude of a divided by the magnitude of W which is square root of six squared plus three squared plus two squared which is seven. To blow it by magnitude away. Now we can cancel magnitude of eight and get the direction designs of the factor W hat, which is the same as a to find because I mean see the eye with the direction of I equals W head dot I Which equals six divided by seven because jaded I equals zero K. Did I equals zero. I did I give you one? Because I in strategy equals W head dot J equals minus three divided by seven. And similarly, we can get design theater Okay, equals W had the key equals two divided by six. We can find the answer as.

Yeah, let's find the scalar in vector productions of beyond A. So we know that the scalar projection is going to be a dot be divided by magnitude today. That's our scalar projection and the vector projection is going to be the same thing, although we're going to square the magnitude and then multiply it times of actor. So with this in mind let's find the projection of beyond A. So first we'll find the the dark power between them. So we're going to use 35 as an example, but we're going to be using this process throughout problems 35 and 40. So we have three times five, which is 15. And then we're gonna be multiplying the next term by zero. So 15 is our product and then we want to know the magnitude of a which is going to be five. So we have 15/5. That gives us three for the scaler And then it's 75 squared is 25. So .6 times are vector, let me 0.6 times three, just 1.8. And then a negative four would give us negative 2.4. So this would be our components for the vector projection

So for us to find these two projections, we just need to plug everything into those formulas they give us in the chapter. So notice how both of them have the dot product of a with B as well as, um, the magnitude of a. So we'll need to go out and find both of those. I'll find the magnitude of a first because that's a little bit easier to do. So we're going to square each of the components Adam together. So negative. Five square plus, um, about 12 12 squared, all square rooted. So that would be 25 plus 1 44 which is 1 69. Just 13. Now to get the dot product So a dotted with B, remember, we're going to multiply each of these components together and then add the results, so we're gonna do negative five times for, and then plus 12 times six. So that would be negative. 20 plus 72 which is 52. Now we just need to plug these in, so over here, it's going to be 50 to over 13, which simplifies down to four. Um, so this is our scalar projection. And then for the factor projection. So again we have 15 or 52 over, uh, will be 13 squares that I just be 13 times 13. And then we have our victor A which is negative 5. 12. So that should simplify down to 4/13, and then we just go ahead and distribute. So that would be negative. 33rd and then 48 13th and then this Here is our sector projection.

In this question, it is told that we have to find the vector projection of. We worked on yogurt, so to find it, we have to use the formula. The formula says that we have to make the dot product of beyond you. And we have to divide by magnitude of use where And then we have to multiply it by You worked also here. Okay. So I'm going to put the value of you and be better. You were 30 years to form a minus one door. This is way better. And you will raise one comma two and delayed by square of magnitude of us. And so you're transformed into this world. One squared plus two. Is where And if that's where we have to do, okay? And we have two multiplied by your weapon. That is one common soldier. Okay? We'll see what happens here further. I can see that if I multiply the dog put up here, then it turns out into going to one minus wanting to do, divide by. we got here five and multiplied by a factor of one or two. So this turns out into zero here and zero multiplied by one comma two. Well, they're here again, zero comma zero. So this is the value or I can say that vector projection or after we on you. Okay? Thank you.


Similar Solved Questions

2 answers
Letr(t) and u(t) be vector-valued functions whose limits exists a5 7C. Prove that lim[r(t) x u(t)] limr(t) x lim u(t) XC (+c LFC Consider the vector-valued functions r(t) = (et sin t)i + (et cos t)j: Show that r(t) andr" (t) are always perpendicular. Prove the property; ifr(t) r(t) is constant, then r(t) .r'(t) = 0. Assume r is a differentiable vector-valued function of t.
Letr(t) and u(t) be vector-valued functions whose limits exists a5 7C. Prove that lim[r(t) x u(t)] limr(t) x lim u(t) XC (+c LFC Consider the vector-valued functions r(t) = (et sin t)i + (et cos t)j: Show that r(t) andr" (t) are always perpendicular. Prove the property; ifr(t) r(t) is constant...
5 answers
Use an F-distribution table t0 fina each of the following F-values. 05 where Vt and Vz Fo.01 where V1 17 and V2 0.025 where VA 35 and Vz = 8 Fo.410 where V1 15 and V2
Use an F-distribution table t0 fina each of the following F-values. 05 where Vt and Vz Fo.01 where V1 17 and V2 0.025 where VA 35 and Vz = 8 Fo.410 where V1 15 and V2...
4 answers
What the conjugate basc of formic (d) For this acld conjugate base, calculate the Kb and the pKb Ethylamine (a) What (CzHsNHz - is the Kb for )isa weak ethylamine base Then calculate (b) Write it's pKb the reaction of ethylamine and water_ (c) What the conjugate acid of ethylamine For this conjugate acid, calculate - the Ka and the pKa.ate the pH of 0 207
What the conjugate basc of formic (d) For this acld conjugate base, calculate the Kb and the pKb Ethylamine (a) What (CzHsNHz - is the Kb for )isa weak ethylamine base Then calculate (b) Write it's pKb the reaction of ethylamine and water_ (c) What the conjugate acid of ethylamine For this conj...
5 answers
148sequence 147 Why identity? are hemoglobin myoglobin; and leghemoglobin considered homologs despite - their 2common for divergent sequences have similar structure?
148 sequence 147 Why identity? are hemoglobin myoglobin; and leghemoglobin considered homologs despite - their 2 common for divergent sequences have similar structure?...
5 answers
Determine whether the integral is convergent or divergentdXconvergentdivergentIf it is convergent; evaluate it. (If the quantity diverges, enter DIVERGES.)
Determine whether the integral is convergent or divergent dX convergent divergent If it is convergent; evaluate it. (If the quantity diverges, enter DIVERGES.)...
5 answers
Rock is projected horizontally from a 70 m tall cliff The range it covers is GOm away from the clfes position: [4 marks; 2 marks each] 2.1 Compute the magnitude of the rock's initial velocity: 2.2 The velocity the rock hits the ground.
rock is projected horizontally from a 70 m tall cliff The range it covers is GOm away from the clfes position: [4 marks; 2 marks each] 2.1 Compute the magnitude of the rock's initial velocity: 2.2 The velocity the rock hits the ground....
5 answers
In plants that lack endosperm in their mature seeds, the cotyledons function to (a) enclose and protect the seed (b) aid in seed dispersal (c) serve as an absorptive embryonic root (d) store food reserves (e) attach the embryo within the ovule
In plants that lack endosperm in their mature seeds, the cotyledons function to (a) enclose and protect the seed (b) aid in seed dispersal (c) serve as an absorptive embryonic root (d) store food reserves (e) attach the embryo within the ovule...
4 answers
(6) (4.5 points) Use Minitab to find the following:(2.5 points) The fitted multiple regression model of regression Ingestion on Weight and Organic. Interpret the estimates of the coeflicients of the explanatory variables in the fitted multiple regression model. points) The associated analysis 0f variance table.
(6) (4.5 points) Use Minitab to find the following: (2.5 points) The fitted multiple regression model of regression Ingestion on Weight and Organic. Interpret the estimates of the coeflicients of the explanatory variables in the fitted multiple regression model. points) The associated analysis 0f va...
5 answers
Evaluate the following integral a8 it is wrilteni[ Xy dx dy (2 +v2)2 Tic Idx dyl (Type an exaci answer
Evaluate the following integral a8 it is wrilteni [ Xy dx dy (2 +v2)2 Tic Idx dyl (Type an exaci answer...
5 answers
11.3.25Qvesbon Holp vJina iollowina andion Ingecaled valuae ol 9KroeonbHonclornunibarIok Find Ihe Marqinel Tovenud functanMardinal rovanue Ior Ihe2429+407 x' q=15,9Inphenal-uttlud tunauon I (Tynd [ lpnanlon Wnino Jlhu variablu ,)
11.3.25 Qvesbon Holp v Jina iollowina andion Ingecaled valuae ol 9 Kroeonb Honclor nunibar Iok Find Ihe Marqinel Tovenud functan Mardinal rovanue Ior Ihe 2429+407 x' q=15,9 Inphenal-uttlud tunauon I (Tynd [ lpnanlon Wnino Jlhu variablu ,)...
5 answers
4wlick is #c sksngestacel? Juskfy Your niwe ko_ CN Ho_ dDrow Hz 3 Yesonance shructuves _ NIz and lobel &ke mujor Conlri e buarDcav H mechansm 8 #g Juwvi = producf, rexehon urel label & _ mjc _HBrOhHt
4wlick is #c sksngestacel? Juskfy Your niwe ko_ CN Ho_ d Drow Hz 3 Yesonance shructuves _ NIz and lobel &ke mujor Conlri e buar Dcav H mechansm 8 #g Juwvi = producf, rexehon urel label & _ mjc _ HBr Oh Ht...
5 answers
What product will form in the following reaction?NBSnone of the aboveWhat set of reagents will best accomplish the following transformation?HBr NBS, Brz Brz Brz, AlBra None of the above
What product will form in the following reaction? NBS none of the above What set of reagents will best accomplish the following transformation? HBr NBS, Brz Brz Brz, AlBra None of the above...
2 answers
Points) The Fourier cosine series of the function f(x) 2x [email protected] cos(kx) k=EFind the coefficients d and @k Your answers might depend on k, and should differ if k is odd or even_When k is odd, @k When k is even, @kYou might use a calculator to graph the function and the first few Fourier approximations to see how the approximation matches the function f(x).
points) The Fourier cosine series of the function f(x) 2x is @k cos(kx) k=E Find the coefficients d and @k Your answers might depend on k, and should differ if k is odd or even_ When k is odd, @k When k is even, @k You might use a calculator to graph the function and the first few Fourier approximat...
5 answers
Problem 16- Use that lim ACioo1) to find 3n*+4 lin 0+4) ACo
Problem 16- Use that lim ACioo 1) to find 3n*+4 lin 0+4) ACo...
5 answers
What is the wavelength of a 21.25 109 Hz radar signal in free space? The speed of light is 2.9979 X 108 m/s. Express your answer to four significant figures and include the appropriate units.AA^ =ValueUnitsSubmitRequest AnswerPart BWhat is the frequency of an X-ray with wavelength 0.14 nm ? Assume that the wave travels in free space Express your answer to two significant figures and include the appropriate units.pAf=ValueUnits
What is the wavelength of a 21.25 109 Hz radar signal in free space? The speed of light is 2.9979 X 108 m/s. Express your answer to four significant figures and include the appropriate units. AA ^ = Value Units Submit Request Answer Part B What is the frequency of an X-ray with wavelength 0.14 nm ? ...

-- 0.023735--