a. What is the angle Φ between vectors E and F in FIGURE P3.24?

Video transcript

Hi, everyone in this practice problem, we're being asked to determine the angle theta formed between the given factors of A and B shown in the figure. The figure is showing a curation, X and Y coordinate where factor A is going from the origin point of zero, comma 0 to 00.1 comma three and factor B is also going from the point of origin zero, comma zero to point minus one comma one, the angle theta is the angle between those two factors of A and B. And another thing that we wanna do is I am going to name the angle from the positive X direction to factor A to be theta A and the angle from the negative X direction to factor B to B theta B because essentially the way we want to calculate theta is by um subtracting theta A and theta B from 100 and 80 degrees. So theta will actually then equals to 100 and 80 degrees minus the A minus the B. The options for the enter choices for theta are 48.4 degrees, 33.5 degrees, 63.5 degrees and 72.1 degrees. So now that we have found our equation that we're going to use to find the, which is 100 80 80 degrees minus data A minus the B, we have to start with calculating what the A and what theta B is the way we want to do this is to by utilizing the in first of tangent. So the A is then going to be the in first of tangent or tangent to the power of minus one of whatever is in front or whatever is opposite over whatever is adjacent. So that will give us a value of three because three is going to be the Y component or what is opposite to the theta divided by A one which is the X component adjacent to the theta A. This will come out to a value of 71.5 degrees. Next, we will have theta B which is also going to be calculated utilizing the inverse of tangent or tangent to the power of minus one. So theta B equals to 10 to the power of minus one of whatever is opposite, which is the Y component, which is one divided by the X component, which is adjacent, which is also one. And they all give us a value of 45°. If you guys are wondering why we're not employing the minus here is because we know what the direction of the, theta B is and essentially what we are curious about is just the magnitude of the angle for theta B. Therefore, we can just neglect the negative sign here. Thus, we can actually substitute all those value into our equation for theta which equals to 100 and 80 degrees minus data A minus the B. So theta will then be 100 and 80 degrees minus 71. degrees minus 45 degrees. That will give us a theta value of 63.5 degrees. And that will be the angle in between factor A and factor B 63.63 point five degrees will correspond to option C. So option C will be the answer to our problem with the angle data formed between the given factors of A and B to be 63.5°. And that'll be all for this practice problem. If you guys still have any sort of confusion, please make sure to check out our other lesson videos on similar topic and that will be all for this one. Thank you.