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Problom 5. polnt) (S. 3-3, ct. no. 1)) Indapendent In R2 : Daterina whethar the tollowing vectors are Ilnaarlyyes() (5) yes() () () yes(0) yesNote: In order to get ...

Question

Problom 5. polnt) (S. 3-3, ct. no. 1)) Indapendent In R2 : Daterina whethar the tollowing vectors are Ilnaarlyyes() (5) yes() () () yes(0) yesNote: In order to get credit for thls problem all answers must be correct

Problom 5. polnt) (S. 3-3, ct. no. 1)) Indapendent In R2 : Daterina whethar the tollowing vectors are Ilnaarly yes () (5) yes () () () yes (0) yes Note: In order to get credit for thls problem all answers must be correct



Answers

Using Equation $(5.1 .15)$ in Problem $22,$ determine all vectors satisfying $\langle\mathbf{v}, \mathbf{v}\rangle>0 .$ Such vectors are called spacelike vectors.

Okay, so we're supposed to use the definition of the ah, this pseudo inner product. Um, and we're supposed to figure out vectors that satisfy vv equals zero. I actually did that at the end of the previous problem, and so we'll just do that again. That's going to be V one. Squared. Whoops. Minus V two squared equals zero. And so, um, if the one equals V two or V one equals the opposite of V two, then, um, the inner product of V and V would be zero. So we could write this solution again as the vector 11 times a constant that would be from here or the vector one negative, one times a constant. And that would be from here. Although the Constance don't have to be the same. So I'm gonna race that, and I'm going to write, um well, d there from my constant

So in the given version we have to find two vectors which I'll opposite direction and also gonna toe the victories like director, who has given us one by two y minus three by 40. Thank So we can like director us one by 23 before let's cells human Director, Director which is how I don't wanna do you vector is in being like so we can find you that we since these two actors about so their dot product has to be Jesus So we get so you get the relation between A and B that is TV to be like Let's take the value of P s too. So we get the values history In this case, the factory is in the three and too late. Let's take an example of base because to minus two So we get a C minus three. So in this case, me is minus three minus too late. So we get the two vectors as three toe and minus three minus two. These two actors in a positive direction and I was gonna do that. You act like

The young version, we have to find two actors which are orthogonal to director and and in a positive direction, right, you rectal, which has given us, uh five by two minus two you like, Let's assume a director is and B which is also going out of you back there since it is all taken out of your actor. So their dot product has to be zero. So we have. So from this equation we get and relation between A and B, that is ah is a close to minus six. So here, minus five right away, So is it goes to minus six by five be like So, uh, let's assume the value of B S five. So you get the value of s minus six as the V vector is minus 65 If the value of B is minus five, the value is six. So he is request of six minus five. Right, So these are the two factors which are all terminal toe you at the end in opposite directions. Right. So we have minus 65 and six minus fight. Thank you.

You're giving You may require five minus two. I love you. The record minus 10 my honesty and things did not need to go. Seven of director minus select start three piece seven of director people required seven or develop remains. One. Oh, my Selling with big minus. It's comes out my seven Goma minus not you. The report we might divide by coma. See my by minus. It's come down the the team comma minus sits no seven of your T minus tree. It is important. Finding seven minus b coma minus 21 less. Six. It is a part my guest among minus not exactly the 90 year of this. This is reporting minus when you this square What is it? Or 54 less Who becomes up where. 70 right? Finally, 10 games in seven


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