Points and vectors

9000101810

Level: 
A
Given points \(A = [1;2]\) and \(B = [4;4]\), find the point \(X\) on the \(x\)-axis such that the distance from \(X\) to \(B\) is a double of the distance from \(X\) to \(A\). Find all solutions of the problem.
\(X_{1} = [2;0],\ X_{2} = [-2;0]\)
\(X = [2;0]\)
\(X = [8;0]\)
\(X_{1} = [2;0],\ X_{2} = [-4;0]\)

9000101802

Level: 
B
Among vectors \(\vec{u} = \left (- \frac{2} {\sqrt{2}};2\sqrt{2}\right )\), \(\vec{v} = (-5;10)\), \(\vec{w} = (2.5;-5)\), \(\vec{r} = (-3.5;6)\) find the vector which is not parallel to the vector \(\vec{a} = (1;-2)\).
\(\vec{r}\)
\(\vec{w}\)
\(\vec{v}\)
\(\vec{u}\)

9000100710

Level: 
A
Given points \(A = [-3;2]\) and \(B = [1;y]\), find the values of \(y\) which ensure the length of the vector \(\overrightarrow{AB } \) equals \(5\).
\(y_{1} = -1\), \(y_{2} = 5\)
\(y_{1} = -1\), \(y_{2} = 1\)
\(y_{1} = 1\), \(y_{2} = 5\)
\(y_{1} = 5\), \(y_{2} = -5\)