Quote:

Given the vectors: .$\displaystyle \begin{array}{ccc}u_1&=&\langle1,2\rangle \\ u_2&=&\langle0,1\rangle \\u_3&=&\langle\text{-}2,\text{-}4\rangle \\u_4&=& \langle\text{-}2,1\rangle \\u_5&=&\langle2,4\rangle \\ u_6&=&\langle\text{-}6,3\rangle \end{array}$

which are:

a) orthogonal?

b) in the same direction?

c) in opposite directions?

My answers

$\displaystyle a)\;\;u_1, u_4,\;\;u_1, u_6,\;\;u_3,u_4,\;\;u_3,u_6,\;\;u_4,u_5,\;\;u_5,u_ 6$ . . . . Right!

$\displaystyle b)\;\;u_1, {\color{red}\rlap{//}}u_2,u_5,\;\;u_4,u_6$

$\displaystyle c)\;\;u_3, u_5,\;\;{\color{blue}u_1,u_3} $