%path = "maths/vectors/2d" %kind = kinda["problems"] %level = 11 \(\vec{x} = \begin{pmatrix}{{g.x[0]}}\\{{g.x[1]}}\end{pmatrix}\) und \(\vec{y} = \begin{pmatrix}{{g.y[0]}}\\{{g.y[1]}}\end{pmatrix}\)
  1. Find the angle between \(\vec{x}\) and \(\vec{y}\)? %chq(0)
  2. What is the area of the triangle created by them. %chq(1)
  3. Calculate their lengths?
    \(|\vec{x}| = \) %chq(2)
    \(|\vec{y}| = \) %chq(3)
  4. Write down the unit vectors:
    \(\vec{x_o} = \) %chq(4)
    %chq(5)
    \(\vec{y_o} = \) %chq(6)
    %chq(7)
  5. Go from the end of \(\vec{y}\) {{g.dx}} units in the direction of \(\vec{x}\) and then back to the beginning of \(\vec{y}\). What is the area of this triangle. %chq(8)