Explanation 1) Concept: i. The equation of the plane is a x + b y + c z + d 1 = 0 ii. The distance between the parallel planes a x + b y + c z + d 1 = 0 & a x + b y + c z + d 2 = 0 is, D = d 1 - d 2 a 2 + b 2 + c 2 iii. The equation of the line in parametric form is, x = x 0 + a t , y = y 0 + b t , z = z 0 + c t , then the direction vector is a , b , c 2) Given: Let L 1 be the line through the origin and the point 2 , 0 , - 1 Let L 2 be the line through the point 1 , - 1 , 1 and the point 4 , 1 , 3 3) Calculation: let L 1 be the line through the origin 0 , 0 , 0 and the point 2 , 0 , - 1 , Then the direction vector of line L 1 is 2 , 0 , - 1 = a , b , c The parametric equation of line L 1 is, x = 0 + 2 t , y = 0 + 0 t , z = 0 + - 1 t x = 2 t , y = 0 , z = - t Let L 2 be the line through the point 1 , - 1 , 1 and the point 4 , 1 , 3 , Then, the direction vector of line L 2 is 4 , 1 , 3 - 1 , - 1 , 1 = 3 , 2 , 2 = a , b , c The parametric equation of line L 2 is x = 1 + 3 t , y = - 1 + 2 t , z = 1 + 2 t The direction vectors of lines L 1 & L 2 are not parallel

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Author: Stewart

Publisher: CENGAGE C

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Question

Chapter 12.5, Problem 79E

To determine

To find:

The distance betweenthe given lines L1& L2

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Chapter 12.5, Problem 78E

Chapter 12.5, Problem 80E

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