00:01
Hi there, so for this problem we are told that the components of a vector are given by.
00:07
So for part a, we have the x component is equal to 3 centimeters, and the y component is equal to minus 4 centimeters.
00:22
First, we need to construct the vectors, find their magnitude and directions, and show them in figure.
00:31
So for this bettore, we are going to construct.
00:35
Construct the vector a, and that is the vector and the x component in the x direction that we put with an unit vector i, plus the y component in the j, with the j unit vector that is in the y component.
00:54
Then this is going to be just simply three in the x direction, minus four in the y direction, these in centimeters.
01:05
Of course.
01:07
Now, if we want to obtain its magnitude, we just simply take the square root of each component to the square.
01:19
So in this case, we will obtain that this is the square root of 25 centimeters square.
01:25
And then this is equal to five centimeters.
01:28
So this is its magnitude.
01:31
And now its direction, we're going to call that the angle theta, we know by 3 .3 .3.
01:37
That the tangent of theta is going to be equal to the y component which is minus four divided by three and then if we want to obtain the angle theta we just simply apply the tangent of minus one to this and then from this we obtain a value of minus fifty three point thirteen degrees now if we want to show them in figure, first what we need to do is to draw an axis.
02:23
This is the vertical axis and the horizontal axis.
02:27
The vertical axis is the white component and the horizontal axis is the x axis.
02:34
Now in this case we know that we have.
02:39
The x component is positive and the white component is negative.
02:43
So that means that this vector should be in the fourth quadrant.
02:50
That means in here...