Unit vector orthogonal to plane

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SUMMARY

The discussion focuses on finding a unit vector orthogonal to a plane defined by the points P = (-4, 5, 4), Q = (-1, 8, 7), and R = (-1, 8, 8). The user calculated the vectors PQ and PR, resulting in PQ = (3, 3, 3) and PR = (3, 3, 4). The cross product was computed, yielding a vector of (3, -3, 0), which was identified as incorrect due to not being a unit vector. The solution emphasizes the necessity of normalizing the resulting vector to achieve a unit vector with a positive first coordinate.

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olivia333
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Homework Statement



Find a unit vector with positive first coordinate that is orthogonal to the plane through the points P = (-4, 5, 4), Q = (-1, 8, 7), and R = (-1, 8, 8).

Homework Equations



u = PQ = Q - P
v = PR = R - P
ans = uXv = PQ X PR

The Attempt at a Solution



so I did:
PQ = Q - P = (3,3,3)
PR = R - P = (3,3,4)

Then I computed the cross product to get the answer.

|i..j..k|
|3 3 3| = <(12-9) , -(12-9) , (9-9)> = <3, -3, 0>
|3 3 4|

The 0 is correct but the 3 and -3 are not. What am I doing wrong?
Thanks!
 
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welcome to pf!

hi olivia! welcome to pf! :smile:
olivia333 said:
The 0 is correct but the 3 and -3 are not. What am I doing wrong?

not a unit vector? :wink:
 
ohhhh haha thank you so much!
 

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