Find all unit vectors parallel to the xy-plane and perpendicular to the vector [1, -2, 2].

so

Using Dot Product

After that i rearrange and get stuck with x-x=0... I don't see any other ways to do this.

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- October 5th 2009, 02:26 PMJimmyRPFind Unit vector parallel to xy plane and perp. to a vector
Find all unit vectors parallel to the xy-plane and perpendicular to the vector [1, -2, 2].

so

Using Dot Product

After that i rearrange and get stuck with x-x=0... I don't see any other ways to do this. - October 5th 2009, 02:44 PMPlato
- October 5th 2009, 04:25 PMKrahl
so you got

so

so the vector

is perpendicular to it but we need it to be a unit vector

its magnitude is

so our unit vector is

=

we get +ve and -ve depending on whether y>0 or <0 i.e two opposite directions which makes sense