5

643 % [[B JOJ EV = (2) [ 414M JOg V XIIQBWI 849 "91! ' $ IOg XIIQBUI pTepue s 34} puuIExv + Ix Ezg + 8zz Ez + 8 + Ir 81 _ II?81 &1 IIKq pauyap &q ...

Question

643 % [[B JOJ EV = (2) [ 414M JOg V XIIQBWI 849 "91! ' $ IOg XIIQBUI pTepue s 34} puuIExv + Ix Ezg + 8zz Ez + 8 + Ir 81 _ II?81 &1 IIKq pauyap &q ,& + && : 4 18T '1 (0z)

643 % [[B JOJ EV = (2) [ 414M JOg V XIIQBWI 849 "91! ' $ IOg XIIQBUI pTepue s 34} puuI Exv + Ix Ezg + 8zz Ez + 8 + Ir 81 _ II? 81 &1 II Kq pauyap &q ,& + && : 4 18T '1 (0z)



Answers

In Problems 79-82, find $\frac{d}{d t}[\mathbf{u}(t) \cdot \mathbf{v}(t)]$ and $\frac{d}{d t}[\mathbf{u}(t) \times \mathbf{v}(t)]$ $$ \mathbf{u}(t)=2 t \mathbf{i}+t^{2} \mathbf{j}-5 \mathbf{k} \quad \text { and } \quad \mathbf{v}(t)=t^{2} \mathbf{i}+2 t \mathbf{j}+\mathbf{k} $$

So in the human christian we have B que en dot the numbers P Q and R. And they are told to be in an april right? They are in an arithmetic progression and we are told to find the value of two delta square minus three delta plus one. Where delta has given us the determinant. 67 P. 78 Q. And 89 are so this is what we need to find, right? So what we're going to do over here is we can take the determinant over here and do some role operation, row and column operations in order to simplify this are determinant, right? So first what we're going to do is we are going to take our one and change it to our one plus our three minus two are so if we do this what we would have us zero zero and he plus I my name is Tokyo right. The rest of the determinant as they say. And now we can easily evaluate this determinant by taking the product people s add minus two q times seven times nine is 63 63 minus eight times eight, which is 64. And this is what we have as the determinant. Right? So this is equal to P plus r minus two, cute times minus one. A polestar minus cube times minus one. Is what we found as the value of the determinant. Right? So let's uh substitute this in the about the equation that we need to find. Right? So what we have is this relation that in if be true and are in an A P. If P Q R p Q and R are in an 80 are in an ap, then we could write that being plus our gives us two Q. So this is a property of three numbers three constitutive numbers in an A P. And we are told in the question that P. Q and R R in an ap. Right? So when we get the determinant of this determinant of this, the determinant given in the question as this, that these people are minus two cube. We knew we know that there is a relation P plus R equal to two cute. Since P Q and R in an 80. Right? So this would then be equal to P plus are can be substituted as too cute. So two q minus two cute times minus one is zero times minus one, which is equal to zero. So the determinant is equal to zero, right? Delta is equal to zero. So in the question we are given to find the value of two deltas career minus three delta plus one. Right? So since delta is equal to zero, the value of this expression would be well to one. So in the question, the option that gives us one as the answer is option B. So option B one is the required solution for the human question. So I hope you invested the method. Thank you.

In this problem I can write the dx n. H. A jeep. A. U. Plus plus e minus changes into a. You. The value of the note is equal to 1.69 b. And the value of A. You change it into a. U. Three plus plus three minus. He not value is equal to -1 40 P. Simplifying it further, I can write the value edge A. U. Plus plus c minus changes in to hey you Au changes into a. U. three plus Plus three E minus for the reaction. H. A. U. Plus changes into a. U. Three plus plus two E minus. So solving it further I will use the formula you know difficult to anyone Even not plus and two. It do not by the end. To putting the value here I can write it as one multiplication .69 Plus three multiplication -1.40 by two Which is equal to -1 25 fight holes. So according to the option option C. It's correct obstinacy. Each that extends it

Okay, so we're asking Add the falling. So let's start with our 1st 2 terms. And actually, it's put our 43288 on top since its larger. And then we have Gates. 2651 So that's 8 to 6 Close. Eight is Fortune. 75678 four and four. And now let's add 53626789 10 11 12 13. Fortune 3456 49 h for four. So we get the following, which is equal to he. Action. Now let's not be there. H So it's, um 448 964 So that's actually de

We are given Vector U and V for U minus three Fee yes, four times you eight minus 20 16 24 Negative 12 minus three times be There's 15 negative six three Negative 21 and negative 12. Do the subtraction between corresponding entries, so eight minus 15 That's negative. Seven. Negative 20 minus six Active. 14 16 minus 3 13 24 minus negative. 21 45 Negative 12 minus negative. 12. That's zero. Part B is similar. Five U plus two v So five times factor you that's 10 negative. 25 20 30 15 plus two times factor V 10 Negative four to negative 14 An active eight so equal to 20 minus 29 22 16 a minus 23 part C We need to multiply corresponding entries to find you that be two times five plus negative five times negative too, plus four times one plus six times negative seven plus negative three times negative four. So 10 plus 10 plus four minus 42 plus 12 Negative. Six. The norm off you is square root off you that you square root of two square plus negative five square plus four square Yeah, plus six square plus Negatives. Three square square root off 90 The norm off We It's also square root off V dot Be the square root off five square plus negative to square plus one square plus minus seven square and plus negative four square square with her 95. The projection off factor you onto V is defined to be you dot be divided by the norm off the square times Vector V We have found you that we does negative six over. Normal fee is square root of 95 square times of actor V Does negative 6/95 times a vector V The distance between U and V is defined to be the norm off U minus. V This is square root off tu minus five square plus negative five plus two square plus four minus one square plus six plus seven square and negative three plus four square square root off nine plus nine plus nine plus 169 plus one that's square root off. 197


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