How to Calculate a Unit Vector Perpendicular to a Plane?

[TW Cantor]

Homework Statement

Given that a = (-1,16,-1) and b = (-18,-15,-15),


find the unit vector which is perpendicular to the plane containing a and b.

There are two possible answers. Choose the answer with a positive x component.

Homework Equations

(a*b) = (a₂*b₃-a₃*b₂)i - (a₁*b₃-a₃*b₁)j - (a₁*b₂-a₂*b₁)k

(a*b)/(|a*b|) = unit vector

The Attempt at a Solution

using the above formula i worked out (a*b)= -255i + 3j - 303K

the modulus of a*b is therefore: sqrt(255² + 3² + 303²)

i then put these values into the equation and i get:

-0.6438i + 0.008j - 0.7651k

since i need to make it positive in the x component my final answer is:

0.644i + 0.008 - 0.765k

am i doing this correctly? it just seems like a very unusual numbers

 

[cupid.callin]

well if there is a vector A then vector opposite to A is -A ... changing only x component makes it something different

 

[cupid.callin]

you can always check if its a unit vector or not,its magnitude should be 1

as this one's mag in approx 1.01 .. i guess your answer is correct