00:01
In this problem, we have been given that there is a vector a, and this vector is added to another vector that's vector b, and it is observed that the resultant vector that is in the positive x direction.
00:18
So here we take i -cap to indicate the direction along x -axis and j -cap to indicate the direction along y -axis, and both of them are unit vectors.
00:28
And when we combine vector a and vector b, that is when we add them, we get the resultant vector, let's say the magnitude of the resultant vector is k and as it is directed along positive x direction.
00:42
So it will be k times i cap.
00:45
And here we are required to get the magnitude of a provided that the resultant vector that is having magnitude same as the magnitude of vector a.
00:56
So let's say the magnitude of vector a, that is just a.
01:00
So instead of k, let's put that.
01:02
So we get vector a plus vector b, which is given as 6 icap minus 8j cap.
01:10
And that's equal to 8 times icap.
01:12
So we have just used this expression to get the resultant vector, because resultant means we just add the two vectors.
01:20
And here we are required to get the magnitude of vector a.
01:23
So let's solve this equation.
01:24
So we will get a vector i cap minus 1.
01:29
We take this a vector to the right and this will be equal to 6 i cap minus 8 j cap.
01:37
Well, let's consider vector a as a into i cap plus b into j cap.
01:45
So it implies that the components of vector a, that is a and b respectively along x and y direction.
01:52
So let's substitute that here.
01:55
And we will get a .i.
01:58
Cap...