Find a vector that points in the same direction as the vector ( î ＋ ĵ ) and whose magnitude is 1.

Video transcript

Hey, everyone. So this problem is working with vectors. Let's see what it's asking us. Vectors can be written in components using unit vectors, determine a vector that shares the same direction as I minus J and has a magnitude of one. Our multiple choice answers here are a one half I plus one half JB one over square of two, I minus one over square root of two J C one over square root of four, I plus one over square of four J, four D one over square rate of six I minus one over square of six J. OK. So we know we have a vector, we'll call it F that has a, that has a direction of I minus J. So when we break that into the components F sub X or the X component of F is one and the Y component of F is a negative one were asked to determine another vector. So we call that factor B that has a magnitude of one. So we have a constant A for I for the eye direction and then we have a constant B for the J direction. And we know that this vector E actually let's use vector notation here. So this vector E has a magnitude of one, which means that the is equal to the square root of the sum of squares. So A squared plus B squared equals one. And so now we can look at our multiple choice answers, there are multiple choice answers. We are given that the A and B constant or I and J. And so when we plug into our calculators, so for multiple choice A we plug in, he equals the swear root of one half squared plus one half squared, we get 0.71 that it's not equal one, it's not the correct answer. B we have one over square of two for B I and J components. So we have one over of two for A plus negative one over of two for B. Put that in, that does equal one. We can look at our C and D answers as well just to make sure that B is the only correct choice. See, it's actually going to be the same as A because one of the square root of sorry, one of the square four squared is the same as one half squared. And so that also equals 0.71, not the correct answer. And D we have, excuse me, E equals one over the square root of six squared plus one over N plus negative one of the square of six squared. And that equals zero. 00.56, which also does not equal one. And so from here, we can see that the correct answer is B because that equals one that, that the vector has a magnitude of one. So that's all we have for this problem. We'll see you in the next video.