Plane Equations Activity.docx - Plane Equations Activity 1...

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Plane Equations Activity 1. 2 x + 4 y + 5 z + D = 0 Passesthrough ( 5,2 , 3 ) 2 x 5 + 4 x 2 + 5 x ( 3 ) + D = 0 D = 17 Equationof planeis , 2 x + 4 y + 5 z + 17 = 0
2. Let equationof planeis ax + by + cz + d = 0 Then, ( 2 , 1,8 ) 2 a b + 8 c + d = 0 ( 5,0,4 ) 5 a + 4 c + d = 0 ( 3,3,5 ) 3 a + 2 b + 5 c + d = 0 2 -1 8 1 R 2 2 R 2 5 R 1 2 -1 8 1 5 0 4 1 0 5 -32 -3 -3 2 5 1 R 3 2 R 3 + 3 R 1 0 1 34 5 R 3 5 R 3 R 2 2 -1 8 1 0 5 -32 -3 0 0 202 28 202 c + 28 d = 0 c = 28 d 202 c = 14 101 d 5 b 32 c 3 d = 0 5 b =− 32 x 14 101 d + 3 d
b = 145 101 d 2 a b + 8 c + d = 0 2 a = 145 101 d + 14 x 8 101 d + d a = 68 101 d The Equationof plane : ( 68 101 x 145 101 y 14 101 z + 1 ) d = 0 ( 68 x 145 y 14 z + 101 ) d = 0 68 x 145 y 14 z + 101 = 0 d ≠ 0
3. a. Since scalarmultiple of any vector alsodenote the samedirection So for different value of normal vectorwemultiply < 3 , 2,5 > by any scalar . Let wemultiply by 2 then normal vectoris < 6 , 4,10 > ¿ 6 x 4 y + 10 z + d = 0 16

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