# Math Help - perpendicular

1. ## perpendicular

Determine a vector perpendicular to both y-axis and the vector with tail at A( 1,1,0) and head at B( 3,9,2) .

2. Originally Posted by fastman390
Determine a vector perpendicular to both y-axis and the vector with tail at A( 1,1,0) and head at B( 3,9,2) .
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so the y axis is <0,1,0> and B-A=<2,8,2>

let <x,y,z> be an aribitary vecotor then

since we want them to be perpendicular their dot products must be zero so

$ \cdot <0,1,0> \iff y=0$

now

$ \cdot <2,8,2> =0 \iff 2x+2z=0 \iff x=-z$

Now we get

$<-z,0,z>=z<-1,0,1>$

so $<-1,0,1>$ is perpendicualr to both.

I hope this helps