Points and Vectors

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 \(5\).
\(y_{1} = -1\), \(y_{2} = 5\)
\(y_{1} = -1\), \(y_{2} = 1\)
\(y_{1} = 1\), \(y_{2} = 5\)
\(y_{1} = 5\), \(y_{2} = -5\)

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 \(\vec{a} = (1,-2)\).
\(\vec{r}\)
\(\vec{w}\)
\(\vec{v}\)
\(\vec{u}\)

9000101803

Level: 
A
In the following list identify a pair of points \(C\), \(D\) such that the vector \(\overrightarrow{CD } \) is not equal to the vector \(\overrightarrow{AB } \) where \(A = [1,3,-2]\) and \(B = [-2,4,3]\).
\(C = [1,-2,3],\ D = [-2,-1,-2]\)
\(C = [6,1,-4],\ D = [3,2,1]\)
\(C = [-3,5,7],\ D = [-6,6,12]\)
\(C = [-3,8,14],\ D = [-6,9,19]\)