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Simply put, a vector is 2 dimensional.
Think of speed - it is only one dimensional. It is not a vector, it is a scalar. It is measured in a scale, most commonly noticed when inside a vehicle. You are travelling at 100km/h (60mph)
Vectors are 2 dimensional, they have a magnitude and a direction.
Think of velocity, as an arrow - imagine you are travelling at 60 mph in a northerly direction, your arrow would be pointing to the notth, with a magnitude of 60mph, If you were travelling at 60mph in a southerly direction, your velocity vector would be pointing towards the south, the exact opposite of your vector if you were travelling in a northerly direction.
However the speed in these two scenario's, speed not being a vector, remains exactly the same, 60mph.
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Positive rotation of a vector is?
counterclockwise
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vector
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What does gradient mean in math terms?
A vector having coordinate components that are the derived during the solving of a function.
Is it true that all physical quantity which has a direction and a magnitude is a vector?
I think so, yes; that's basically what the concept of a "vector" in physics is all about. (There are also more abstract vectors in math and physics, but something that has a magnitude and a direction would be enough to quality as a vector.)
What is the difference between vector and algebraic sums?
A vector has both a magnitude and a direction. To add vectors, you graphically put them head-to-tail; or, to do it with math, separate the vector into x and y components, and add the two components separately. Or more than two components, depending on the number of dimensions used.
What is the differentence between calculus and vector calculus?
Hence the reason for why it is called Vector Calculus, Vector Calc. is simply an expansion in the calculus subject are in math. It deals with Taylor's Formula (in calc 2 you learn the taylor polynomial and the taylor series), theorems from Green, Gauss, and Stokes, and much more.
