in this video we're going to talk about the difference between a scalar quantity and also a vector quantity so when you think of these words what comes to mind what is the difference between these two terms a scalar quantity is something that has magnitude only but a vector quantity has both magnitude and direction so if you think about the word magnitude basically it's the size of something or its numerical value direction has to it carries the idea of something traveling in a certain direction like east west north or south so here's the question for you distance is it a scalar quantity or is it a vector quantity so think about distance is a scalar quantity if a car travels let's say five miles you don't know in what direction it's going so that would represent distance however let's say if a car travels five miles east so now you have the distance with direction which is known as displacement displacement is a vector quantity because direction is part of displacement whereas distance it's a scalar quantity now what about speed is speed a scalar quantity or vector quantity so let's say if a bus is traveling at 30 miles per hour is that a scalar quantity or is that a vector well we don't have direction so it's a scalar quantity now let's say if the car is moving at 40 miles per hour north now we have speed with direction that is known as velocity so velocity is a vector but speed is a scalar quantity so velocity we describe it as let's say 30 miles per hour east the 30 miles per hour that is the magnitude that's how fast is moving it's the numerical value the direction part of the vector is east so you got to have those two parts magnitude and direction for a quantity to be a vector if an object is simply traveling at 30 miles per hour with no direction then we only have magnitude only which makes it a scalar quantity not a vector quantity so if you can apply direction to something that makes it a vector if direction cannot be applied to it then it's a scalar quantity so here's another example force is force of vector quantity or is it a scalar quantity you can apply 50 newtons of force east west north or south so force has direction you can push an object you can push a box to the right you can lift it up you can push it towards the north direction so force is a vector quantity now what about mass which column would you put mass under the left side or the right side can you apply direction to mass can you say i have 100 grams of aluminum metal east or 200 grams of nickel west you can't apply direction to mass therefore mass is a scalar quantity how about temperature is temperature a scalar quantity or is it a vector quantity so can you have a temperature of let's say 90 degrees fahrenheit east or 100 degrees celsius west direction is not part of temperature it has there's no association so therefore temperature is a scalar quantity it only has magnitude it doesn't have any direction the magnitude could be 90 degrees fahrenheit 100 degrees fahrenheit of course 100 is much higher than 90 but as you can see temperature you can only describe it in terms of magnitude only you can't describe it in terms of direction you can't say it's 85 degrees fahrenheit east outside it just doesn't make sense now what about acceleration is acceleration a scalar quantity or is that a vector quantity acceleration is a vector quantity acceleration tells you how fast your velocity is changing with respect to time so if you're driving a car a car has a greater acceleration than a truck both a car and a truck can go from zero to 60 miles per hour but a car can get to that speed a lot faster than the truck so a car has more acceleration now you can accelerate towards the east towards the west north or south so direction can be applied to acceleration which makes acceleration a vector quantity now what about volume would you describe volume as being scalar or a vector can you have 50 liters of water east or 2 gallons of milk west direction cannot be applied to volume so volume is a scalar quantity so now you know how to distinguish if something is a scalar or vector quantity the key is to focus on direction because both scalar and vector quantities have magnitude but only vector quantities have direction so if direction can be applied to something then that something is a vector now there are different ways to describe a vector you could say that 100 newtons of force is applied at let's say an angle of 30 degrees relative to the x-axis so you can apply you could describe a vector by describing in terms of its magnitude and direction which the first example illustrate you can also describe it graphically so let's say this is the x-axis this is the y-axis so we have a force of 100 newtons at an angle of 30 degrees relative to the x-axis so you can also describe the magnitude and direction graphically another way in which you could describe a force is by expressing its components so you could say its x component is 30 newtons and its y component is 60 newtons so let's call this f x and f y and the graph looks like this so let's say the red line is f x it's 30 and the blue line is fy which is 60. so it's twice as long but because both are positive they're both in quadrant one so this is f the hypotenuse of the right triangle is the actual vector and this is f of x it's the x component of f and this is f y the y component so let's say if f of x was negative 40 and f y is 60 where would you draw this vector so first you would have to travel 40 units to the left to describe f x because it's negative x is negative on the left side now f y is positive 60 so you got to go up 60 units and so f is in quadrant two so if you know the components you can describe the vector let's see if f is 200 newtons but at an angle of 2 25 degrees so if you have to graph it this is 0 90 180 and 270. so 225 is in quadrant three so the vector is going to be over here and this is an angle of 225 relative to the x-axis when dealing with vectors you might find these equations useful so the hypotenuse is the actual vector f this is f of x f of y and the angle theta now if you have the x and y components and you need to find f you can use this equation it's based on the pythagorean theorem if you need to find the components you can use this f y is f times sine theta f of x is f times cosine theta and if you need to find the angle this is an acute angle between 0 and 90 you can use the arctan or the inverse tangent formula it's f y over f of x and if i was you just make f of x and f of y positive and this will give you the reference angle or the angle between 0 and 90 that's within this triangle and then you can always adjust the angle based on what quadrant it should be located in but these four equations can help you to find missing quantities associated with vectors so that's it for this video thanks for watching and have a great day you