Linear algebra Let D1 and D2 be two concurrent lines of R2. (a) Find the coordinates of the intersection point of D1 and D2. (b) Give the angle formed by these two lines. (c) What is the distance between the point X(5,3) and D1? Sketch the situation and explain your calculations by giving the meaning of each of the elements of the formula used. (for example: |u • v x w| gives the volume of the parallelepiped generated by u, v and w)
Linear algebra
Let D1 and D2 be two concurrent lines of R2.
(a) Find the coordinates of the intersection point of D1 and D2.
(b) Give the angle formed by these two lines.
(c) What is the distance between the point X(5,3) and D1? Sketch the situation and explain your calculations by giving the meaning of each of the elements of the formula used. (for example: |u • v x w| gives the volume of the parallelepiped generated by u, v and w)
(d) What are the coordinates of the point P E D1 which is closest to X? Tip: Represent the situation to understand what calculations need to be made.
(e) Find the coordinates of X', the mirror image of X, i.e. the "mirror image" of X. This is the point that lies on the other side of D1 at the same distance from D1 that X and such that X, P, X' are on the same line. Tip: again, represent the situation to understand what calculations need to be made.
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