For the two vectors in Fig. E1.35, find the magnitude and direction of (a) the vector product A x B

Video transcript

Hey everyone welcome back in this problem. We are asked to find the vector magnitude and direction of the vector product M times end of the two vectors below the vectors below that were given in the diagram we have the vector M. Which is a length of 3.2 m and it's 48 degrees above the positive X axis. Okay, So it's in the first quadrant and then we have vector A. And vector N is in the fourth quadrant. It has a length of 2.3 m. It is 48° below the positive access access. Sorry. Alright. So when we're thinking vector product, another term for this is cross product. Okay, what we want to start with is the direction we want to find the magnitude and direction. Let's start with the direction. Well, to find the direction, we want to use the right hand rule. All right. Now, if we do the right hand rule, we wanna place our fingers pointing in the direction of em. Okay, We're gonna curl them towards the vector N. And we're gonna look at where our thumb is pointing. Okay, So if we do that in this case our thumb is gonna be pointing into the page. Okay, So we're going into the page and that is going to be the negative Z. Direction. Okay. All right. Now, what we're talking about magnitude, let's look at the magnitude of C and C is going to be that cross product or the vector product of the vector M. And the vector N. Ok. Now recall that the vector product. The magnitude of the vector product can be given by the magnitude of the vector, M magnitude of an times sine of data. Ok. And in this case data is going to be the smallest angle that you can find between the two vectors. Okay, so in this case data is going to be this angle here. The magnitude of that angle. That's the theater that we want to use. Alright. So let's get started With. The magnitude of em we're told is 3.2 m. The magnitude of N. We're told is 2.3 m and sine of theta. And again, data is this total angle here. So it's going to be 48 degrees plus 48 degrees. We have 48 degrees plus 48 degrees. Is gonna be the angle between M and N. Okay, so working this out, we're gonna get 7.36 times sine of 96°. And that's gonna give us 7.32 meters. Okay. Alright. So now we know our magnitude the magnitude of our vector product, the direction was minus C. Okay. And so we're gonna have answer A The magnitude is 7.32 and the direction is minus Z. Thanks everyone for watching. I hope this video helped see you in the next one