Unformatted text preview: ˆ’1 2 0 ï¿½ = 6Ë† + 3Ë† + 2k.
Ä±
j
ï¿½
ï¿½
ï¿½ âˆ’1 0 3 ï¿½
â†’ âˆ’ ï¿½ 1ï¿½ 2
â†’ï¿½
1 ï¿½âˆ’
1âˆš
7
ï¿½âˆ’
Then area(Î”) = ï¿½P Q Ã— P Rï¿½ =
6 + 32 + 22 =
49 = .
2
2
2
2
â†’
âˆ’
âˆ’
â†’âˆ’
â†’
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b) A normal to the plane is given by N = P Q Ã— P R = ï¿½6, 3, 2ï¿½. Hence the equation has the form
6x + 3y + 2z = d. Since P is on the plane d = 6 Â· 1 + 3 Â· 1 + 2 Â· 1 = 11. In conclusion the equation of the plane is
6x + 3y + 2z = 11.
â†’
âˆ’
c) The line is parallel to ï¿½2 âˆ’ 1, 2 âˆ’ 2, 0 âˆ’ 3ï¿½ = ï¿½1, 0, âˆ’3ï¿½. Since N Â· ï¿½1, 0...
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This note was uploaded on 01/21/2014 for the course MATH 18.02C taught by Professor Denisauroux during the Fall '12 term at MIT.
 Fall '12
 DenisAuroux
 Multivariable Calculus

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