Given vectors1.007 00j ad B = 3.007 +4.00j the maznitude and the directicn of vector c-3.00A 2.00B are:4.11 and 33.70 clockwvise from tne positive X-axis4.11and 33....

The two vectors $\vec{a}$ and $\vec{b}$ in Fig. 4-23 have equal magnitudes of $10.0 \mathrm{~m}$. Find (a) the $x$ -component and (b) the $y$ -component of their vector sum $\vec{r},(\mathrm{c})$ the magnitude of $\vec{r}$, and $(\mathrm{d})$ the angle $\vec{r}$ makes with the positive direction of the $x$ axis.

Hi in this problem. First, we will draw the diagram. In this diagram we have given a vector. A is in negative by access direction like this. This is Victor A. And the magnitude of this factor is given, which is 8 m. And the vector B is given like this. Yeah, this is after me. And the magnitude of Victor B is also given to us, which is 15 m in length. And this angle from the positive by access is also given, which is 30 degrees. Right? So first we have to find a vector plus V. Victor, we know that we can write. A vector is equal to eat meter and direction minus Jacob like this. We can also right. Victor B is equal to 15 Scient I d. I kept plus 15 cost 30 Jacob Now in part A. We have to find a victim, plus the victim. Now this will be equal toe 15 sign 30 I kept plus 15 cost 30 minus eight. Jacob, If we solve this with the help of calculator, we can get the venue. 15, 7 30 is equal to 7.5 I kept. Plus this 15 cost 30 minus eight will be equal to around 4.99 Or we can say five. Jacob, this is the value off a vector plus V vector. Right now in part B. We have to find Victor a minus. Vector B. Victor a minus. Sector V will be equal toe. Eat minus. Jacob minus 15. Sign 30 minus 15. Cost 30. Jacob. Right. So this will be equal toe minus 7.5 ICAP minus mhm 21. Jacob, this is the value off a vector. Minus the victim. This is Jacob. Now we have to find in part C minus a minus V.

Okay for this problem we're going to find minus a plus B. So just you that just just compute right minus a final three. Why does one and plus minus one so over to right? Happy. So just modify or what have each couple. So just add a lot minus four on a, uh Right. So for the back into, we can just use for me. I asked 16 plus one force, right, A squared plus B square and squirt. So just 16 plus, that should be, Ah, four point 03 That is actually Ah, squirt 65/2. Hey, you can just write this answer and don't use this approximately Announcer So I think right. Scored 65/2. That's enough. Hey, that's fine. The broth for this. So minus war one should be something like this. Here is one. Have and here's for so we can calculate for this angle here. That is to the our for our first should be arc attendance are contingent 1/2. Divided by 41 or eight. Right? So what else? There should be seven point one degree. Okay, so this weighs very small. So we can we can use this. This is Sabra Sita. And did this angle here should be our direction angle. So stay. There should be 180 minus. This are for which is why 170 two point. I agree, okay?

Okay, so if we use the information given, we can write the two vectors sound. Start with a A is 3.2 magnitude, um, co sign of 63 in the J hat direction, plus the sign of 63 in the K hat direction be 1.4 times the co sign of 48 in the eye had direction, plus a sign of 40 hat in the K A direction. Okay, um, if we resolve all this stuff out, we get 1.45 j hat plus 2.85 K hat in 0.937 I had plus 1.4 k hat. All right. If we do, um, we do the dark product scaler product a dot oh, a dot B. There's only one component in comment. That's the cake opponents. Um, so is that's the only thing that's gonna contribute to the dot product. So it's gonna be 2.85 times 1.4 but just equals, um, 2.97 cross product. Um, here, we're gonna have a couple of things contribute. So the we just write this whole thing out, it's gonna be a why b z minus a busy bee. Why, I had who? Us a Z b x minus a x b z j hat plus a x Be why minus a y b x. Okay. Hat. Okay, um, we can get rid of this term a Z B y. Because we don't have a B y, we can get rid of this term. It does not have an x component. And we can get rid of this term again because A does not have an X component. Um, so we end up with is 1.51 I waas 2.67 j but minus one 0.36 Okay, hot. The angle between A and B is given as coast in verse of the dot product over the product of the magnitudes. This is the coast inverse of 2.97 over 3.2 times 1.4, which is equals 48 0.5 degrees

For this problem, we are given um values of and be and we're asked to find the magnitude of the resultant From these two forces or two factors. Rather eventually, this will be useful when calculating forces. So we have the inverse tangent of the over A. That allows to find the angle measurement between A and B. And then we have the square root of iceberg plus B squared. That allows to find the magnitude of the resultant vector from the vectors A and B. So once we understand this, were allowed to plug in our values of A. And B. So that way we can determine the value of the magnitude and the value of Ceta. So our magnitude is going to be equal to when we put in A equals 1734 and B equals 3297. See magnitude is 3200 or 3725. And the angle measurement is 62.26°..