![]() Same thing as the ratio up here so we're going Going to have, one way to think about it the ratio between these two numbers is the exact The horizontal direction and four fifths in the vertical direction. To, the magnitude we already figured out is five so it's going to be three fifths in Once again we justĭivide by the magnitude, magnitude of our vector. ![]() It's three in the horizontal direction, four in the vertical direction. It's going to be equal toĮach of these components, for A we just divideīy the magnitude of A. Instead of this littleĪrrow when you put this hat this denotes that you'reĭealing with a unit vector, a vector with magnitude of one. To also make it clear it'sĪ unit vector and not just a normal vector I'm going On top I'm going to put - Actually just to not confuse ourselves let's call it U for a unit vector. Vector, I'll call it A but instead of putting an arrow Way of thinking about it, if we divide each of theseīy the magnitude of A then we can construct this unit vector. Of these components of our vector A by a fifth, or another What could we do? If we scale everything down by a fifth, if we were to multiply each Another way of thinking about it, let's say we wanted to figure out a vector that goes in theĮxact same direction but it has one fifth the magnitude, it only has a magnitude of one. Let's say we wanted toĬonstruct a unit vector that has the same direction as A but Right over here is five so I could say the magnitude You might have just recognized that this would be a three, four,įive right triangle. Square root of nine plus 16, square root of 25, or it's going to be equal to five. Squared plus four squared or this is going to be the This length is going toīe the square root of the sum of the squares What's its magnitude? The magnitude is just the length of this vector right over here and we can use the Pythagorean theorem to figure this out. In the horizontal direction we're going to go four in The magnitude of vector A, well this would just be the length of it. What else do we know about this? We could figure out A's magnitude, we can denote it like this. Vector, let's say the vector A, and in the horizontalĭirection for every three that it moves in the verticalĭirection it moves up four. A unit vector is justĪ vector that goes in a particular direction that ![]() What I want to do in this video is explore the idea of a unit vector.
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