5

El6 IOamnmueueuehiephpwUbow p in thelfigura below And defingd by the vectors u = (,0,0)" ToumkoULkea#HHPolsLo4 2} # mllece eliscanceis quensured in centimeters...

Question

El6 IOamnmueueuehiephpwUbow p in thelfigura below And defingd by the vectors u = (,0,0)" ToumkoULkea#HHPolsLo4 2} # mllece eliscanceis quensured in centimeters:MUEEEAEELAE MHLE pua4uhnihe6 #hehHLhal p Lhalpau aHelephned WEWGIW Eeoe 6E hulluehukumeipeehepelelelepieth

El6 IOamnmueueuehiephpwUbow p in thelfigura below And defingd by the vectors u = (,0,0)" ToumkoULkea#HHPolsLo4 2} # mllece eliscanceis quensured in centimeters: MUEEEAEELAE MHLE pua4uhnihe6 #hehHLhal p Lhalpau aHelephned WEWGIW Eeoe 6E hulluehukumeipeehepelelelepieth



Answers

Given the vectors $\overrightarrow{\mathbf{P}}$ and $\overrightarrow{\mathbf{Q}}$ shown on the
grid, sketch and calculate the magnitudes
of the vectors (a) $\overline{\mathbf{M}}=\overrightarrow{\mathbf{P}}+\overline{\mathbf{Q}}$ and $(\mathbf{b})$
$\overrightarrow{\mathbf{K}}=2 \overrightarrow{\mathbf{P}}-\overrightarrow{\mathbf{Q}} .$ Use the tail-to-head method and express the magnitudes in centimeters with
the aid of the grid scale shown in the drawing.

In this exercise, you have the two vectors that are shown here in the screen. And given the defectors, we have to use the component the components of these two vectors in order to find in question a the value of a plus B. And I'm gonna call this vector, See, just, uh, in order to make things easier. So the first thing we need to do is to ride the vectors in their component for the way is equal to X. I was a y J where I and J are the unit vectors in the UAE annex directions, respectively. So this is Jay. This syriza will I I noticed that the vector a forms a rectangle triangle whose legs are a why and a X and who's both a news is a that is the magnitude of the that. So a raise equal to the magnitude of the vector times the coal sign Yes. Of 60 I bless benefit of the vector. Time to sign of 60 g sweetie is 2.8 times the cool side of 60 I plus 2.8 times the sign of 60 j. So a 0.4 i class okay, 2.4 j centimeters. While B also forms, everything will triangle. But notice that in this time, uh, me x is positive. But be wise. Negative. So the likes of legs of the rectangle triangle O r the magnitude of B Why and the just be X So the movie will be the magnitude v times a cold sign off 60 i Mine is the main It'd be time sign of 60 g so v is equal to 1.9 times the court fine of 60. That's the X component minus won't wait nine times a sign of 60 which is the wife important. So V is equal to zero point 95. I might as 1.6 c five g So are two vectors are here and in question A. We have to talk to the sea, which is a place to be and this is ah component by component in the X important we have 1.4 plus 0.6 c Uh, where's your point? 95 centimeters and in the X component will have 2.4 minus 1.65. So C is equal to 2.35. I it was 0.75 g and we want to find the magnitude and direction off. See, so the members of C is the square root off 2.35 squared for 0.75 square, and this is equal to 2.47 centimeters then in question. But you have to find the vector see which is equal to a minus bi, so have to subtract component by component. You have 1.4 minus zero point dining five I plus 2.4 plus 1.65 g. So C is equal to 0.45 I plus four point old five g, which means that the magnitude of C is equal to the square root of 0.45 square was four 0.5 squared and this is equal to four point old seven centimeters. Uh, now we have to find the magnitude of these two vectors, that which is found so in question A. I noticed that the vector see as a positive has, uh, positive accident. Components of electricity is pointing in first bother it and we want to find this angle here, said the tensions off ADA is, um, the white important divided by the ex important meeting that that data will be the art, its engines of C wide about it. I see ex. So this is the ark tensions of 0.75 where I hadn't right right here. So it's the attention off 0.75 The very body 2.35 is this equal to 17.7 degrees. In the second case in question V again, the again the vector is in the fillers crab quadrant, and we want to find the angle. So the tensions of feta is see wide whenever see X meaning that later will be the our attentions of see why which is 4.5 divided by, ah, see acts which is there went 45 and this is equal to 83.7 degrees Questions. See, we have to do the same thing, but with a vector that is equal to be mine, is it? What is that? Demon is a is just minus a minus B. And since the vectors only differ, um, for a for a minor side sign, then the magnitude is the same, meaning that the magnitude of this of after C is equal to the magnitude of a minus B, which is equal to 4.7 centimeters. And notice that if the vector April's V is this one here in the first quadrant is a please be in vector Sorry, a minus bi. The letter B minus eight is just this in vector but reflected. So this year is a human is a so this angle failure that would comfort before is the same as this angle here. So is that the angle that the vector makes with the the X X is fine is equal to theta close 180. So have one on 180 plus 20 actually, 80 3.7, so five is equal to 263.7 degrees, and this is the end to our exceptions.

If we're given to Victor's and B if you say use our usual location off horizontal axis being X axis on vertical axis being waxes, we see that Vector A makes an angle of sixty degrees with the X axis and has a length off two point eight centimeters on DH. Vector B also makes an angle of sixty degrees with the X axis, but has a length off one point nine centimeters. Now before we go ahead with it, the problems Let's write down the vector forms off just A and B before I forget. This is Victor, eh? And this is victory now for better, eh? The better. It would be just two point eight centimetres, multiplied by cost. Sixty. I can't That's two point a sign sixty Jacob, which turns out to be one point for a cab that's two point for tow chicken. Similarly, for Let There Be, the ex component is similar. It is one point nine multiple because sixty but the Wycombe parent is downwards, which is negative, and Steve Component will be minus one point nine sign sixty chika, which turns out to be zero point nine five minus one point six for Jake. You can notice that because car sixty is half this number is half off this number. Similarly here. No. Let's start with Victor. A velocity now, Victor, eh? Is something like this on Victor. Be is something like this. Now, if you translate this victor over here and write again, we can see that it would look something like this. Now, this will be our result in Victor. No, By using competent meter, we just aren't the individual components. And write a Frisbee by adding the ex competence. One point for Felicity on nine five. I can't less one for two minus one word. Six for chicken. Excuse us two point three five. The cedar point seven eight. Jake. Now the magnitude ofthe this vector is simply the square root of the sun off squares of the component. It is through two point three by scared zero one seven eight square, which gives us for one zero eight units. And the anger tannin worse off the component. Zero one seven eight derided by ex comfort and coupon three five gives us eighteen point three sixty, please. Now, looking at the diagram, this seems pretty reasonable. This angle is bound to be smaller. It's pretty small on eighteen degrees seems to be a good number. And when we compare the X and the white confidence off this victor, we see that the ex conference is very large, whereas one component is not that large, which is a reflector here. Now let's go to the next doctor. A minus B now doing the subtraction. Confident wise, we can write it US one point four minus one nine five. I can't less two point four two minus off minus one point six four Gica by doing this math teacher until Toby zero point four five plus four point zero six Jacob Now the happy to the length ofthe suspect er is simply the square root off the sum of the squares of the conference. It is here. One for five square is four point zero six squared, which turns out to be or point zero eight. I'm sorry, but this number is not four point zero eight. It turns out to be who want for eight Now getting back to this problem, we can find the angle it makes with the X axis as an inverse x com Perrin. I'm sorry. Quite confident you read it by ex confident, which turns out to be eighty three on six eight degrees. Now let's try drawing this now better. Eh? Is like this Victor be is like this, but minus factor minus B would be something like this. And if we add, might just be the way it would look something like this on the result in Victor would be something like this. We were expecting much larger. Why component? Compared to the X Company, which is seen here on the angle, we expected to be pretty large, which is seen here almost pretty close to ninety degrees. And this is straightforward. Now let's go to the next part, which is B minus C. Now we do the same confident ways suppression again, and we can see that it is equal to zero one four five. Wanna sit upon for six Jigga I'm sorry. Minus one for my cap minus four point zero six chacha, if you notice this is equal and toe minus off Emily's fee. If you didn't wear what a minus B wass If you're doing what or came on his b wass, it was this. You can see that it is D minus off that victor. Now, if you try to diagram now, before you go ahead, the magnitude would be expected to be the same as a minus B because the components I just I have the same may be good, but how The same flick on DH The magnitude turns out to be the same. Now the angle, though it's different. We know that this Viktor exists in the third quadrant. I'm we can show that the angle is equal to dying. Words four point zero six by zero one four five which is the component divided by X company. Notice that we have neglected the science here would be eighty three point six degrees. But this angle it would make with negative X axis and in the downward direction and the language makes with the boss to exact sis would be one eighty plus this angle my regardless let's try toe, draw these pictures. Now we know the victor is something like this. I'd better be is something like this Now my vector minus C would be something like this. If we add this vector, Toby, it looks something like this. And hence our result in Victor would be something like this. This would be a B minus. As you can see, we expect a much larger white component compared to the ex component, which is evident here. And we expect both of them to be negative because it is. This is in the third quarter, which is also true. And we expect this angle to be very close to ninety degrees. Because this angle things were his fault on eighty three point six eight degrees, which is the angler makes with the negative X axis. This angle is very close for ninety to this, it seems to justify our answers.

Hi in a given problem, we have been given a vector victor, a bar whose magnitude Is given us 20 meter and Its angle is 25° and this angle is always encounter clockwise direction from the positive X. Axis. So to show the diagram for this vector we use, first of all, we use a scale and we draw the access. This is the X axis. Sorry, this is y axis and then this is the X axis, X. Axis and Y axis. Now in order to show the length of this vector one cm will represent one centimeter. A. Here in our diagram will represent 10 m. So here to represent 20 m we should use the length of 2cm and we will take a scale, our protector Having a value of 25°.. It will start from the origin and the length should be equal to two centimeter. This is one and then two centimeter. So this is the answer for this given problem. Here this land two centimeter representing the vector A. At an angle of 25 degree from positive X axis, encounter clockwise direction. Thank you

In this problem we have given vector A. It is a cost to 4.5 cm. This is the magnitude and the direction is given 40 centimeter ever the positive X axis. Suppose this is positive X. Axis. And this is a factory And this angle is given which is 40°.. So we will convert it into the component form. So we can write this is a cost to 4.5 cost 40 in X cab direction plus 4.5 signed 14. Why can't direction? So we can find 4.5 in two cars 40. This is a cost to to the point. Yeah. 45 30 point four or 5 x cap plus 4.5 multiply with signed 40. So this is a cost to 2.90. Oh, I kept. This is the component form of victory. Yes, now in the second part we have given another vector B which is two cm in Xscape direction minus four centimeters in the vicap direction. So we can find the magnitude of this vector, which is the cost to Do you square plus four square. The square is four. was 4square is 16. So this is to route five which is a cost to four wind 47 centimetres. Now, if we talk about that direction, so this is V. X. And this is we buy. So this is the anger civil strata. So we can find this rita will be called to 10 and verse B. Bye bye VX. So this three to will be equal to 10 and verse Viva is four x 2. That means this is standing worse too. This angle theta is a call to 63 four degree below the positive X axis. Thank you. Mhm. Yeah. So we can say the magnitude of vector B is 4.47 centimetre and direction of this victim is 63.4° envelope the positive X axis. Now we have given another victim which is a cost to eight centimeter at an angle 60 degrees. Mhm. This is director see magnitude is he would send doing it and it is ever 60 degree the negative X axis. This angle is theater Which is a cost to 60 deal. So we can write into the component form. So this will be equal to eight costs data in the -X cap direction Plus eight Science data in the positive. I can't direction. So This is a cost to -8 cost 60 escape plus eight science 60 vicap. So better see is a cost to eight into cost 60 which is four plus eight into Sign 60 which is 6.93. This is the continent form of vectors. So that's it. Thank you.


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