![]() You would not want to thrown in a pesky direction, would you? I mean, does it really make sense to say that I want 4 kilograms of watermelons facing West? Unless you are some crazy fanatic, of course. That's when you use a "regular" number (something like 4 or 1/3 or 3.141592653 - nope, for all you OCD freaks, I am NOT going to put Pi there - that shall stay a terminating decimal, just because I am evil incarnate). So, the above discussion clearly says that we need unit vectors to define other vectors, but why should you care?īecause sometimes, only the magnitude matters. There are other forms of coordinates (such as Cylindrical and Spherical coordinates), and while their coordinates are not as direct to understand as (x, y, z), they too are composed of a set of 3 mutually orthogonal unit vectors which form the basis into which 3 coordinates are multiplied to produce a vector. They are the basis of all Cartesian coordinate geometry. i, j, and k are unit vectors in the X, Y and Z directions and they form a set of mutually orthogonal unit vectors. (Note: I will no longer call them by caps, I'll just call them i, j, k). Any vector we think of as V = (x, y, z) can actually then be written as V = xi + yj + zk. These reference directions are canonically called i, j, k (or i, j, k with little caps on them - referred to as "i cap", "j cap" and "k cap"). Turns out, to define a vector in 3D space, we need some reference directions. But what do we really mean by Cartesian coordinates? Note however, that all the above discussion was for 3 dimensional Cartesian coordinates (x, y, z). Hence, unit vectors are extremely useful for providing directions. Also, every vector pointing in the same direction, gets normalized to the same vector (since magnitude and direction uniquely define a vector). vectors with unit length).Īny vector, when normalized, only changes its magnitude, not its direction. Hence, we can call normalized vectors as unit vectors (i.e. It is easy to see that a normalized vector has length 1. ![]() When we normalize a vector, we actually calculate V/|V| = (x/|V|, y/|V|, z/|V|). For any vector V = (x, y, z), |V| = sqrt(x*x + y*y + z*z) gives the length of the vector. ![]()
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