How do I find a vector perpendicular to a line that passes through these two points?

I need a vector, any vector, that is perpendicular to the line that passes through [0,0,0] and [9,2,1]??





How would I find one?





Any help is appreciated!|||tHE LINE HAS A DIRECTION D= (9,2,1) -(0,0,0) = (9,2,1)





a perpendicular vector ( see Gram -Smith process) may be obtained from any vector .-


Suppose the vector V .- The projection over D is Vd = IVI cosT T angle between both .-


cos T = D dot V / I DI I VI , ie Vd= IVI cos T = D dot V / IDI , BUT in the D direction , ie on the unit D direction %26lt;D%26gt; = D / IDI





Vd= IVI cos T %26lt;D%26gt; = ( D dot V / IDI^2 ) D





Then Vd + Vn = V , Vn is the normal component of V .- we are looking for just Vn .-


Vn= V- Vd


Vn= V -( D dot V / IDI^2 ) D





Take any vector , V= i D dot V= 9 , IDI^2 = 81+4+1= 86





Vn= i - (9/86) (9,2,1)





Vn= ( 5/86 , -18/86 ,-9/86)





Check , Vn dot D = 45/86 -36/86- 9/86 = 0 ok /