Find 2 vectors that are orthogonal to v=

Question

Find 2 vectors that are orthogonal to v=<2,-3>

anonymous · Answer

Recall that orthogonal vectors will have a dot product of 0. $$\implies <2,-3>\cdot = 2a + -3b = 0$$ Pick some solutions.

anonymous · Answer

ya but i got two unknown

bobbyleary · Answer

Orthogonal essentially means perpendicular. One way to visualize this is by plotting <2,-3>, then drawing a perpendicular to this. One solution is <-3,-2>. To check your answer, the dot product of these vectors must equal zero, so <2,-3>(dot)<-3,-2> = 2*-3 + -3*-2 = 0. polpak will give you a better solution though...:)

anonymous · Answer

is it possible if i want to get the answer by calculation?

anonymous · Answer

Having two unknowns just means that there is a whole bunch of solutions.

anonymous · Answer

$$2a - 3b = 0 \implies 2a = 3b \implies b = \frac{2}{3}a$$

Pick any a you like.  Make b be 2/3's of that. Boom, orthogonal vector.

anonymous · Answer

ok ..thx