# Vector shoot --- Introduction ---

This is a visual exercise on the linear combination of vectors (linear algebra): given a set of vectors ${v}_{1},...,{v}_{k}$ and a set of scalars ${a}_{1},...,{a}_{k}$, the linear combination

$u={a}_{1}{v}_{1}+{a}_{2}{v}_{2}+...+{a}_{k}{v}_{k}$

is a vector.

Therefore the exercise gives you the vectors ${v}_{i}\in {ℝ}^{2}$ described graphically in a figure, as well as the concrete values of the coefficients ${a}_{i}$. And you are asked to click on the point in the figure which you think is the end of the vector $u$ (a shot).

At the end of a session composed of several shots, you will be given a score computed according to the average precision of your shots during the session.

The difficulty of the exercise varies with the choices of several parameters.
• Number of vectors: 5  (The difficulty increases with the number of vectors).
• Range of variation of the coefficients ${a}_{i}$ :
• Number of shots in one session: 10  (The score is given only at the end of a shooting session).
• Density of the grid (0 = no grid): 10  (A fine grid facilitates the location of vectors.)

You may also go to the exercise by a simple choice of the level of difficulty.

Other exercises on:

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