Consider the plane, ccP in RR^3 by the vector equation x(s,t)=(1,−1,2)+s(1,0,1)+t(1,−1,0);s,t in RR Compute a unit normal vector, n, to this plane.

GepGreeloCesyjk

GepGreeloCesyjk

Answered question

2022-09-24

Consider the plane, 𝒫 in 3 by the vector equation
x ( s , t ) = ( 1 , 1 , 2 ) + s ( 1 , 0 , 1 ) + t ( 1 , 1 , 0 ) ; s , t
Compute a unit normal vector, n, to this plane.
My attempt is the third normal vector is ( 1 , 2 s t + 1 , 1 ) and the unit normal vector I got is
1 3 + 4 s 2 t 2 + 4 s t ( 1 , 2 s t + 1 , 1 )

Answer & Explanation

Edward Chase

Edward Chase

Beginner2022-09-25Added 10 answers

HINT
n = ( 1 , 0 , 1 ) × ( 1 , 1 , 0 ) ( 1 , 0 , 1 ) × ( 1 , 1 , 0 )
EDIT
Since ( 1 , 0 , 1 ) = i + k and ( 1 , 1 , 0 ) = i j , one has that
( 1 , 0 , 1 ) × ( 1 , 1 , 0 ) = ( i + k ) × ( i j ) = k + j + i = ( 1 , 1 , 1 )

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