orthogonal vector

[forest venture]

Find the orthogonal vector to vector u=[3,-1,4] using dot product

[rocky hound]

well there are infinite many

[forest venture]

Hm okay how do I get an answer though

I have emailed my teacher about this question they did say there is infinite answers

I can show you exactly what they said

[sacred valve]

adonhs

[rocky hound]

If you know how dot product works you would get this:

||3x -y +4z = 0 which is a plane containing infinite many vector||

[forest venture]

This is what my teacher said

Choose any number for x and y solve for z

and I don’t know what to do after solving for z

[rocky hound]

your teacher just copied me

[forest venture]

he sent this response like days ago I think you copied him 🤔

[rocky hound]

then you got all three components for the orthogonal vector

[forest venture]

well yes

[rocky hound]

well then there is the answer 😄

[forest venture]

I don’t get it though it though I solve for z and then I have all the components for the orthogonal vector how can I prove that it is orthogonal, just out of curiosity

[rocky hound]

you already proven it

your result is a plane

a plane that contains infinite many vectors being orthogonal

by choosing x = 1 and y = 1 for example, we are looking for the according z value that fits

that's it

[forest venture]

How come there are infinite answers? Just asking out of curiosity again because in an ordered pair it’s just the negative reciprocal

[languid quest]

isnt plane just a locus of multiple coplanar vectors?

[rocky hound]

because you get a plane

[forest venture]

okay

[rocky hound]

and a plane spans a vector space

I drew one vector as an example

[forest venture]

this makes a lot of sense thanks

[rocky hound]

you have basically 3 variables left, which means there is a lot of variety to choose one orthogonal vector

[forest venture]

Thanks a lot

[rocky hound]

if that was it, you can close the thread with .solved

[rocky hound]

.solved