Question

how do i find all unit vectors orthogonal to v=<3,4,0>

Answer 1

u.v=0... all vectors

Answer 2

\[u _{1}+3=0\]\[u _{1}=-3\]

Answer 3

err... wait... hmm....

Answer 4

\[3u _{1}+4u _{2}=0\]

Answer 5

we need another equation....

Answer 6

u1² + u2² = 1

Answer 7

what pops to mind is u cross v divided by magnitude u cross v

Answer 8

okay... so given your vector... there is no z... so the slope in the floor is y/x or 4/3
a perpendicular slope would be -3/4 which leads to <4,-3,0> or <-4,3,0> as perpendicular vectors in the floor.
to make them unit vectors in the floor we would divide by the magnitude to get\[\frac{1}{5}<4,-3,0> or \frac{1}{5}<-4,3,0>\]in the floor.

Answer 9

now, how do we get a z component....

Answer 10

\[\frac{1}{\sqrt{25+z ^{2}}}<4,-3,z> or \frac{1}{\sqrt{25+z ^{2}}}<-4,3,z>\]