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Question

If the vector $\mathbf{A}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}$ and the vector $\mathbf{B}=4 \hat{\mathbf{i}}-5 \hat{\mathbf{J}},$ what angle does $\mathbf{A}$ $+$ B form with the $x$ -axis?
(A) $	heta=	an ^{-1} \frac{3}{5}$
(B) $	heta=	an ^{-1} \frac{7}{5}$
(C) $	heta=\sin ^{-1} \frac{3}{5}$
(D) $	heta=\sin ^{-1} \frac{5}{7}$

Sachin Rao · Accepted Answer

this problem we have given Vector is equal to I kept minus two. Jacob Vector B is equal to for a cab minus five jackets so we can find Vector A plus. Victor, we This will be called to ICAP plus four ICAP minus two. Jacob minus five. Jacobs, this is a quality of five by cab minus seven. Jacob Now we will draw this vector. This is suppose X axis and this is why access. So in the Y axis, it is negative seven. And in the X axis, it is five. So vector, will we? This vector is a vector. Plus rejected. We have to find this angle. So according to 10 data, 10 data is equal to perpendicular, which is equal to seven divided by five. So Tita will be called to 10 and verse seven by five. If we check our option option, we will be our correct option. Option V. Thank you

Abdul Vahid M · Answer

sure. 27 and big. Listen, teaching and you don&#x27;t deflated at you Go. It exists. I mean, direct presents again. So what happened? Just pull it. Senses and reflexes. But somebody to different mistaking Exactly. Well, you have to find me. It&#x27;s only going to get Yes, I know it is open and you can find sanguine people, you know? No. When he reached up second, this gave me because it&#x27;s against our people. No. What kind of this find Come back in this. That they let&#x27;s see. Thank people. Well, people come down on this one. Big hearing the same. So here also, you&#x27;re gonna be in points. So what? When you get here, this buying or something departed? Get minus four point. Oh, the seven. No. Did they? But the undersigned you have to find it. They do get us a victory. I am Jacobovitz, Listen. State vector here. Come back. Come on. This I understand everyone. Six. See, we do know that by now on a typical picking Cambone evidence so that you and Victor this to a point. It&#x27;s itchy

Willis James · Answer

lesson lesson. We&#x27;ll finally younger between two vectors A and B. So do this by finding the dot product, and that has given us the magnitude of vector eight times the magnitude of vector B cause Sita, where zika is the angle between two vectors. So here we&#x27;ll make that cost fee to the subject of the equation So we can divide both sides by the magnitude of the vectors, so that this will cross out that then we have the costs of the angle as a dot be all over the magnitude of a the magnitude of the Okay. So here the cost theater is equal to Yeah, the doctor border took the back test 5 to 1, then the magnitude of them. Uh huh. Oh, so in the dot product, you would multiply the correspondent cams, then you some them some of the correspondent times. Oh, Okay, so here we have one plus nine plus 16. Okay, so that keeps us 26 then. Here we have 25 plus four plus one. That gives us 30. Okay, so the course of the angle, it&#x27;s negative. Five last six plus five, all of us, the square root of All right. 780. That is 30 times 26. Okay, so we have the cost feature of that is four. So five negative five. Last six gives us one plus four. That gives us what&#x27;s going on. That gives us five. Oh, so five over square root of 780 Okay, so to get a theater, we take that course or five on the square root of That&#x27;s Okay. So the articles of 0.1 79 0 to 9, and that is 79 0.686 793 08 to 1 degrees. And this is opposed. Made leaf 80 degrees. Okay, so the angle between the vector A and Vector B supposedly eat the grease. Okay. Thanks for time at the end of the lesson.

Jason Li · Answer

given position factor negative to negative five. We want to do the three for going so well. First graphic. So given position factors, you know, way start a 00 So we only have toe move according to visiting a factor. So negative too. So to to allow negative five. So five down. And this is our We also know that since quadrants are labeled one to three. Four, we see that her factor is in quadrant three. So our quandary It will be home. A new moral three now for magnitude? No, that this is a right angle triangle. So give in pathetic gris We also know about this is by an ex. So you know that I want a factor. It&#x27;s equal to this. Were why X squared plus y squared. Industrious people too. The square of negative. Too good. It&#x27;s negative. Five squared, which is equal to the square four plus 25 which is equal to square root of 29. School magnitude is 29. No, to find our data did the closest X axis. We see that it is here. So this opr data, we can either during this geometrically we see that will first find this angle and will subtract 90 dignities of this will subtract that angle from 90 degrees. So we have opposite, which is acts over a Jesus, which is why so we get Tad is equal to opposite, which is X bridge case. Why? So we get paid, uh, is equal toe Eric Tan X and why five? And now we got, uh, has answering an absolute values. We get Mark 10 to you 90 degrees minus 10 to 5. Since it is, we are trying to find us.

Ankit Gupta · Answer

now question is asking. Bet the remind the direction Ingle Peter off the victor to the nearest degree in the Given Better is you is equals to minus two minus fight and it&#x27;s we know that he dies. It was toe then into us. Reto, divided by we will hear re to women is like the victor. We won. We do so here will have the teat. Isaac was too standing Waas minus five duet by minus two, which is five. Do I didn&#x27;t buy do This really will be close to 68 0.19 They fight. So this is the angle which we need now Question is asking to the nearest Diggory. So this is the nearest Viguerie. Now let&#x27;s see the question or you can say the next part of the question.

Problem

An object travels along the vector $d_{1}=4 \math…

Problem 6 Easy Difficulty

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