Question

Find the vector ⃗⃗v that is orthogonal to vector u. Look at attachment.
⃗⃗⃗

Answer 1

orthogonal means the dot product of two vectors is 0

\[<x,y,z> * <2,y_o,-3>\]
\[2x + y_o y -3z = 0\]
let y = 1/y_o , so that term = 1
\[2x +1 -3z = 0\]
let x = 1, z=1

so vector v is ...
\[<1, \frac{1}{y_o}, 1>\]

Answer 2

big thanks!!

Answer 3

Could you help with another orthogonal problem? Its attached to this message I get <1,0,1> as my answer but i'm not sure its correct.

Answer 4

unit vectors must have a length of 1
\[\sqrt{x^2 +y^2 + z^2} = 1\]
now set up both equations from using dot product
\[x+y-z = 0\]
x -z = 0 ---> x = z
plug into first equation
z+y-z = 0 ----> y = 0

ok so your answer is orthogonal , however it is not a unit vector
plug x=z , y=0 into distance formula
\[\sqrt{x^2 + 0^2 +x^2} = 1\]
\[\sqrt{2x^2} = 1\]
\[x^2 = \frac{1}{2}\]
\[x = \frac{1}{\sqrt{2}}\]

Answer 5

I wasn't using the distance formula! I truly appreciate your help.

Answer 6

:)