Finding perpendicular vector

PhizKid

1. The problem statement, all variables and given/known data

Find a unit vector in the xy plane which is perpendicular to A = (3,5,1).

2. Relevant equations

[tex]
A_x{B_{x}} + A_y{B_{y}} + A_z{B_{z}} = \textbf{A} \cdot \textbf{B}\\\hat{\textbf{A}} = \frac{\textbf{A}}{|\textbf{A}|}
[/tex]

3. The attempt at a solution

In order to be perpendicular, A•B = 0 since a perpendicular 90 degrees would mean cos(90) = 0, so the entire dot product becomes 0.

So:

[tex]\textbf{A} \cdot \textbf{B} = 3{B_{x}} + 5{B_{y}} + 1{B_{z}}[/tex]

But since B doesn't exist on the z plane:

[tex]\textbf{A} \cdot \textbf{B} = 3{B_{x}} + 5{B_{y}}[/tex]

So:

[tex]0 = 3{B_{x}} + 5{B_{y}}[/tex]

Not sure what to do from here. Using:

[tex]\hat{\textbf{B}} = \frac{\textbf{B}}{|\textbf{B}|}[/tex]

How would I turn this B vector into a unit vector?

ehild

How do you get |B| from the components?

ehild

andrien

you can take (1/√34)(-5i+3j) as your unit vector.
edit-or also 5i-3j in place of -5i+3j.

Chestermiller

If B is a unit vector, then B dotted with B has to be 1. What does this mean in component form?