# Math Help - vectors

1. ## vectors

What is the z component of a vector parallel to the x-y plane ? explain
find all unit vectors parallel to the x-y plane and perpendicular to the vector [1,-2, 2 ]

2. Originally Posted by fastman390
What is the z component of a vector parallel to the x-y plane ? explain
find all unit vectors parallel to the x-y plane and perpendicular to the vector [1,-2, 2 ]
In $\mathbb{R}^3$ any vector in the xy plane has no vertical component so its z component is zero.

for part two

is the vector is parallel to the xy plane it is perpendicular to the z axis

again let <x,y,z> be any vector so we know that

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

$ \cdot <1,-2,2>=0 \iff x-2y=0 \iff x=2y$

so we get

<x,2x,0> =x<1,2,0>

To make this a unit vector divide each component of the vector by the vectors magnitude!