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which of the following can represent a vector so a vector is something that has both a magnitude and a direction so let's see which of these could represent something that has a magnitude and a direction so the first choice right over here is the number 5 well 5 could represent a magnitude you could say essentially how large something is but it that's all the information has it doesn't say 5 in a certain direction so this one by itself would not be a or it couldn't represent a vector you need you need to specify a direction as well the angle measure 5 degrees well the angle measure 5 degrees could represent a direction if you say it's 5 degrees let's say that's the positive x-axis that's the positive y-axis if you said it's 5 degrees relative to the positive x-axis so if you said something like this so if you had 5 degrees right over there that wouldn't be specifying a direction but it's not giving us a magnitude it's not saying how far in that direction or how large in that direction so an angle measure of 5 degrees you're giving us a direction but no magnitude so let's just cross these out the point 5 comma 5 now this is interesting if if we say that the point is the end point of a vector that started that starts at the origin so let's draw that out so if that's the positive x-axis positive y-axis if this is see 1 2 3 4 5 in the horizontal direction 1 2 3 4 5 in the positive vertical direction then the point 5 comma 5 is going to be is going to be right over there and so if you said that this represents the essentially the head of a vector that whose tail is at the origin so the vector would look something like this now you're giving both a magnitude and a direction what's the magnitude what's the distance between the origin and this point right over here which you could solve using the Pythagorean theorem and the direction is this this the direction that that I've just drawn the vector it's this general it's that general direction so this is best or this could specify a magnitude and a direction so this could represent a vector the outcome of five plus five well obviously that's just ten that's just a number and for the same reason this first choice if I just have a number that could be a magnitude but we don't have a direction as well so this could not represent and that one could not represent a vector