1.
\(A=(1,0)\) and \(B=(0,1)\)
Exercises 1.13 Exercises
Exercise Group.
Given are two points \(A\) and \(B\text{.}\) Find the vector representation \(\overrightarrow{AB}\text{.}\) Furthermore, find \(2\cdot\overrightarrow{OA}\text{,}\) \(-1\cdot\overrightarrow{OA}+3\cdot\overrightarrow{OB}\text{,}\) and \(\overrightarrow{OA}-\overrightarrow{OB}\text{.}\)
2.
\(A=(0,1,-2)\) and \(B=(0,1,-1)\)
3.
\(A=(a_1,a_2,a_3)\) and \(B=(-1,1,0)\)
Exercise Group.
Given are two points \(A\) and \(B\text{.}\) By considering vectors \(\overrightarrow{OA}\) and \(\overrightarrow{OB}\text{,}\) find their dot product and their respective lengths.
4.
\(A=(2,3,1)\) and \(B=(-1,2,0)\)
5.
\(A=(2,2)\) and \(B=(1,-1)\)
6.
Let \(A=(1,-1,a)\in\C^3\text{.}\) Find \(a\in\C\) so that the length of \(\overrightarrow{OA}\) is \(1\text{.}\)
Exercise Group.
Given are two points \(A\) and \(B\text{.}\) Consider vectors \(\overrightarrow{OA}\) and \(\overrightarrow{OB}\) to find the angle between them. Check whether they are perpendicular to each other or not.
7.
\(A=(2,1)\) and \(B=(1,1)\)
8.
\(A=(-1,2)\) and \(B=(-2,4)\)
9.
\(A=(1,-3,2)\) and \(B=(3,1,-4)\)
Exercise Group.
A point \(A\) is given. Find a point \(B\) so that the vectors \(\overrightarrow{OA}\) and \(\overrightarrow{OB}\) are perpendicular.
10.
\(A=(2,-1)\)
11.
\(A=(3,3,-1)\)
12.
\(A=(-1,-1,-1)\)
