Question

Can you find all unit vectors perpendicular to (0,3,4)

Answer 1

Yes, I can :D
Can you? ^.^

Answer 2

I have found 2, but apparently there is more?

Answer 3

Much more :)
Two vectors are going to be perpendicular if their dot product is zero.

Answer 4

So...

\[\huge <x,y,z>\cdot<0,3,4> = 0\]
\[\huge 0x + 3y + 4z = 0\]

Answer 5

Well, have you gotten it from here? :)

Answer 6

I have gotten (0,4/5,-3,5) and (0,-4/5,3/5)

Answer 7

I require one more to complete my question

Answer 8

Okay... thinking :)

Answer 9

But isn't there like, infinitely many unit vectors perpendicular to that vector?

Answer 10

I assume so, but I'm having trouble visualising and providing a third unit vector

Answer 11

Well, here's the thing...
0x + 3y + 4z = 0
Well, 0x = 0, you can leave that part out
3y + 4z = 0
So, as long as your y and z value fit this, it should be fine.
Get three possible pairs of values for y and z.
Of course, you can pick any x value, it doesn't matter.

And you'll have as many vectors as you want that are perpendicular to your vector, but then again, not all of those are unit vectors (maybe not one of them at all)

Just divide them all by their respective magnitudes and you're all set
That's it.

Enjoy.

Answer 12

I will! Thanks for the help