Explanation Given information: The equation of plane is 3 x − 2 y + z = − 1 a and point is P ( a , 2 a , 3 a ) & a ≠ 0 Formula Used: Distance of a point P ( x ∘ , y ∘ , z ∘ ) from a plane a x + b y + c z + D = 0 is given by d = | A x 0 + B y 0 + Cz 0 +D | A 2 + B 2 + C 2 Calculation: It is given that equation of plane is 3 x − 2 y + z = − 1 a o r 3 x − 2 y + z + 1 a = 0 On comparing with A x + B y + Cz+D = 0 A = 3 , B = − 2 , C = 1 & D = 1 a The point is P ( a , 2 a , 3 a ) = ( x 0 , y 0 , z 0

6th Edition

ISBN: 9781465208880

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 9.6, Problem 21PS

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To find: Distance of a point P(a,2a,3a) from a plane 3x−2y+z=−1a .

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Chapter 9.6, Problem 20PS

Chapter 9.6, Problem 22PS

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1. Find the two points on the x-axis which are at a distance 2 from 3x – 4y – 6 = 0. a. (16/3,0), (-4/3,0) b. (15/2,0), (-2,0) c. (5,0), (-1,0) d. (4,0), (-1,0) 2. The line 3x-y+6=0 is midway between two parallel lines which are 4 units apart. Find the equations ofthe two lines a. 3x - y + 610 = 0 b. 2x - 3y + 610 = 0 c. 3x - y + 6210 = 0 d. 3x - y + 65 = 0 3. The points A(1, 0), B(9, 2) and C(3, 6) are the vertices of the triangle, which of the following is an equationof one of the medians? a. 4x - 5y = 6 b. 4x + 5y = 4 c. 4x - 5y = 4 d. 4x + 5y = 6 4. Three consecutive vertices of a parallelogram are (-4,1),(2,3) and (8,9). Find the coordinate of the fourthvertex. a. (2,7) b. (3,8) c. (2.1,7) d. (3,6)

Chapter 9 Solutions

Calculus

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Distance of a point P ( a , 2 a , 3 a ) from a plane 3 x − 2 y + z = − 1 a .

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Chapter 9 Solutions