Let A = 2i + 3j, B = 2i - 4j, and C = A + B. (b) Draw a coordinate system and on it show vectors A, B, and C

Video transcript

Hey, everyone in this problem, we're asked to use vectors M which is equal to three I plus five J and N which is equal to four I minus six J to calculate P which is equal to M plus N, a graphical representation to show all three vectors. So let's start with M and N, let's see if we can eliminate any of these answer choices based off the graph for those. So M is three I plus five J. That means the X component is three, the Y component is five. If we go to our diagram, we can see that all four answer choices A through D show M being with an X component of three and A Y component of five. OK. So we can't eliminate any of our choices based off of that. And same thing with N or I minus six J, an X component of four A Y component of negative six J. If we look at our four answer choices, all of the N vectors are drawn just like that X component of four Y component of negative set. So I haven't enter drawn correctly on this diagram. What it's gonna come down to is this vector P that we need to calculate. We're gonna go down and give ourselves some blank space to work out this vector P. And we're told that P is gonna be equal to ma and recall that when we're adding vectors, we can just add the components, say the corresponding component. So we have M plus N, this is gonna be equal to three I plus five J plus four I minus six J and just substituting in the values we were given for these vectors. Now, for the X component, OK, we wanna add the I components together. So we have three I plus four, I, that's gonna give us seven I and for the J components, we have five J plus negative six J and that's gonna give us minus J. And so our new vector P is gonna be seven I minus J. We want our vector to be seven I minus J and we want to see this on the graph. So we wanna be looking for an X component of seven A Y component of negative one going up to our diagram. OK. In option A, this looks good. OK? We have seven I minus J. The vector P has an X component of seven A Y component of negative one. So that one looks correct. Let's just double check with the rest to make sure that this is in fact the correct answer. In option B, we have a positive Y component, which is not what we found. KP is in quadrant one. So that one's incorrect. Same thing with option CP is in the wrong quadrant for option DP is in the correct quadrant, but the components are not correct K, the Y component is far too large at negative 7.8. And so A is indeed the correct answer. K, it has the correct vector for P seven I minus J and all three vectors are drawn correctly in that diagram. That's it for this one. Thanks everyone for watching. See you in the next video.