00:01
Here we have to use the graphical method to find out the resultants.
00:07
So basically this is very easy question.
00:12
So first of all we will look after this one.
00:16
So i am talking about a, b, c, d and f.
00:28
So for a, let us talk about that.
00:32
So now this is a.
00:34
So now what is like x component, horizontal component? it would be a cos theta.
00:42
That is a, that is 10 cos 30 degrees.
00:49
Right? so this is basically what? this should be 10 cos 30 means we have root 3 by 2 multiplied by 10.
01:06
This gives us 5 root 3.
01:10
Right? now we have this one, the vertical component.
01:18
What will be the vertical component? vertical component would be 10 sin 30 degrees.
01:27
So what is sin 30? sin 30 is going to be 1 by 2.
01:33
So 10 by 2 means what? this should be 5 itself.
01:37
Right? we got it simply.
01:39
So we need to like this is xy.
01:42
Okay, this is xy, y and this is x.
01:46
Right? so this should be positive and this should be positive.
01:49
Other should be negative if it is in left hand side or downwards.
01:54
Okay, so that is very important.
01:56
Now we have another one for c part.
01:59
Let us see.
02:00
So for c part it is the cos component comes here.
02:05
That is making an angle.
02:06
Okay, 60 degrees.
02:08
So it should be 120 cos 60 degrees.
02:14
What is cos 60? cos 60 means 1 by 2 itself.
02:19
So it means that it is equal to 60.
02:22
Now if you talk about this one, that means it should be minus sign.
02:27
Okay, 120 sin 60.
02:30
What is sin 60? sin 60 means root 3 by 2.
02:39
Root 3 by 2 multiplied by 120.
02:42
That means that gives us equals to minus 60 root 3.
02:48
Right? so this is very important things we are talking about.
02:52
Okay, now here we have for f.
02:57
Let us say we have this is sin component.
03:01
So this will be in downward side.
03:03
That means it will be negative sign minus 20 sin 30 degrees.
03:15
Right? so what is sin 30? sin 30 is a half of it like this is equals to 1 by 2.
03:26
Right? so it becomes minus 10 here.
03:30
Now if you talk about this cos component, so it should be 20 cos 30.
03:40
So what is cos 30? cos 30 is going to be root 3 by 2 multiplied by 20.
03:47
So what is that? this gives us the value.
03:51
This should be negative sign.
03:53
Remember, so it should be minus 10 root 3.
03:58
Right? now for similarly for b we will calculate.
04:02
This is positive.
04:03
So that is b cos b sin.
04:06
A vertical component would be b sin 53.
04:09
So that means 5 sin 53 degrees, which is equals to what? which is equals to sin 53 is nothing but it will be 0 .798 multiplied by 5.
04:33
Right? so this gives us 3 .99.
04:37
Right? now this will be cos component also there.
04:42
So cos component would be 5 cos 53 degrees, which is equals to cos 53 is 0 .60 multiplied by 5.
04:58
So this gives us 3 .00.
05:02
Right? now for d also we will find the similar things.
05:06
So here we have d cos that is 20, 20 sin here, 20 sin 37 degrees.
05:21
So what is sin 37 degrees? sin 37 degrees is 0 .60 approximately multiplied by 20.
05:31
This gives us 12 .03.
05:35
Right? now this is cos component.
05:39
So it should be 20 minus 20 cos 37.
05:43
So it should be equals to cos 37 that is equals to 0 .79 multiplied by 20, which gives us 15.
05:56
Minus 15 .97.
06:00
Right? now this became very easy to understand.
06:05
Now these are the like coordinates you have to remember and what we have to find out.
06:11
I'll tell you first of all, it is as for a plus b.
06:16
Right? a plus b.
06:21
Remember here our directions matter a lot.
06:25
So here i have written in ij format that is on the terms of position vectors along with the direction so that you may understand that what is the direction, whether it is positive on the or on the negative side of the x and y axis.
06:45
Right? so now this is what we have abcd vectors and f.
06:55
These are the values.
06:56
They are very important here.
06:58
Now we need to find out first of all, first problem is a vector a plus vector b.
07:08
So what is vector a? vector a is 5 root 3 i cap plus 5 j cap.
07:14
Correct? plus 3 .0 i cap plus 3 .99 j cap.
07:25
Correct? so now what it becomes is 5 root 5 root 3 right? plus 3.
07:38
So that gives us somewhere 11 .66 value...