Consider the plane, ccP in RR^3 by the vector equation x(s,t)=(1,āˆ’1,2)+s(1,0,1)+t(1,āˆ’1,0);s,t in RR Compute a unit normal vector, n, to this plane.

GepGreeloCesyjk 2022-09-24 Answered
Consider the plane, š’« in ā„ 3 by the vector equation
x ( s , t ) = ( 1 , āˆ’ 1 , 2 ) + s ( 1 , 0 , 1 ) + t ( 1 , āˆ’ 1 , 0 ) ; s , t āˆˆ ā„
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 )
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Answers (1)

Edward Chase
Answered 2022-09-25 Author has 10 answers
HINT
n = ( 1 , 0 , 1 ) Ɨ ( 1 , āˆ’ 1 , 0 ) ā€– ( 1 , 0 , 1 ) Ɨ ( 1 , āˆ’ 1 , 0 ) ā€–
EDIT
Since ( 1 , 0 , 1 ) = i + k and ( 1 , āˆ’ 1 , 0 ) = i āˆ’ j , one has that
( 1 , 0 , 1 ) Ɨ ( 1 , āˆ’ 1 , 0 ) = ( i + k ) Ɨ ( i āˆ’ j ) = āˆ’ k + j + i = ( 1 , 1 , āˆ’ 1 )
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