I learned the fundamentals of vectors and basic (e.g. addition, dot product) vector operations in a Trigonometry course, and they're being reintroduced in the Physics I course I just began.
My question is about the method for manually adding or subtracting two vectors, by placing the second vector at the tip of the first vector, and drawing a third vector from the tail of the first vector to the tip of the second one. (My summary of the method here may be somewhat vague or perhaps inaccurate, but that's beside the point of my question).
How can this method provide any acceptable degree of precision? For most people, drawing/sketching is not an innate skill. Each individual will draw the same vector addition operation slightly differently.
Without the aid of technology, it would be virtually impossible to draw, say, a vector with a magnitude of 3 meters and a vector with magnitude of 5 meters, perfectly to scale so that the resulting vector sum would be precise.
For these reasons, I've always been a bit skeptical of the method. It is, however (of course), the standard method, which tells me that I'm wrong to be skeptical of it.
What's the point of all this, if not to arrive at a precise answer? Is this just a case of needing to know the fundamental technique now, and having it superceded by a more sophisticated technique in a more advanced, future course? I mean, is it just me, am I missing something, or is this technique of vector addition (when performed by hand) almost totally random and subjective?
Drawing to get the solution is not the standard method. The standard method is just to add the entries of the vector one-by-one, shown here in the case of two-dimensional vectors: $$\pmatrix{a \\b}+\pmatrix{c \\d}=\pmatrix{a+c \\b+d}$$