math192_hw2sp06 - HW2 Solutions 12.5 Lines and Planes in...

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Unformatted text preview: HW2 Solutions 12.5 Lines and Planes in Space 2. x = 1- 2 t, y = 2- 2 t, z =- 1 + 2 t . 6. x = 3 + 2 t, y =- 2- t, z = 1 + 3 t . 22. 3 x + y + z = 5 31. n 1 n 2 = vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle i j k 2 1- 1 1 2 1 vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle = 3 i- 3 j + 3 k is a vector in the direction of the line of intersection of the planes 3( x- 2) + (- 3)( y- 1) + 3( z + 1) = 0 3 x- 3 y + 3 z = 0 x- y + z = 0 is the desired plane containing P (2 , 1 ,- 1). 36. d = radicalBig 14 3 is the distance from S to the line 44. d = 3 2 2 is the distance from S to the plane 56. 2 x- 3 z = 7 2(- 1 + 3 t )- 3(5 t ) = 7 - 9 t- 2 = 7 t =- 1 x =- 1- 3 , y =- 2 , z =- 5 (- 4 ,- 2 ,- 5) is the point 13.1 Vector Functions 4. v = 6 j and a =- 4 i at t = 0 8. for t =- 1 , v (- 1) = i- 2 j and a (- 1) = 2 j for t = 0 , v (0) = i and a (0) = 2 j for t = 1 , v (0) = i + 2 j and...
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This note was uploaded on 02/05/2008 for the course MATH 1920 taught by Professor Pantano during the Spring '06 term at Cornell University (Engineering School).

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math192_hw2sp06 - HW2 Solutions 12.5 Lines and Planes in...

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