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## 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) = (a

_{2}*b

_{3}-a

_{3}*b

_{2})i - (a

_{1}*b

_{3}-a

_{3}*b

_{1})j - (a

_{1}*b

_{2}-a

_{2}*b

_{1})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(255

^{2}+ 3

^{2}+ 303

^{2})

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