Points and vectors

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

9000101808

Level: 
B
Consider a parallelogram \(ABCD\) with \(A = [1;3]\), \(B = [2;-1]\) and \(C = [5;1]\). Let \(S\) be the center of the diagonal \(BD\). Find the vector \(\overrightarrow{AS } \).
\(\overrightarrow{AS } = (2;-1)\)
\(\overrightarrow{AS } = (2;1)\)
\(\overrightarrow{AS } = (1;3)\)
\(\overrightarrow{AS } = (-2;1)\)

9000108701

Level: 
B
Find all vectors which are perpendicular to the vector \(\vec{u} = (3;4)\) and have the length equal to \(1\).
\(\left (\frac{4} {5};-\frac{3} {5}\right )\), \(\left (-\frac{4} {5}; \frac{3} {5}\right )\)
\(\left (\frac{4} {7};-\frac{3} {7}\right )\), \(\left (-\frac{4} {7}; \frac{3} {7}\right )\)
\(\left ( \frac{1} {\sqrt{10}};- \frac{3} {\sqrt{10}}\right )\), \(\left (- \frac{1} {\sqrt{10}}; \frac{3} {\sqrt{10}}\right )\)
\(\left (\frac{4} {5}; \frac{3} {5}\right )\), \(\left (-\frac{4} {5};-\frac{3} {5}\right )\)