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4- Find parametric and symmetric equations of the line passing through the points (1,- 1,2) and (2,1,5). Tind

4- Find parametric and symmetric equations of the line passing through the points (1,- 1,2) and (2,1,5). Tind

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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4- Find parametric and symmetric equations of the line passing through the points (1,- 1,2) and (2,1,5). 5- Find the distance from the point s(1,-6,2)to the line x = 2 + 3t, y = -4 + t,z = -2t Ans >>d=1.79 6- Find the distance between the skew lines defined by L1: r(t) =< 1+t,2 + 6t, 2t > L2: r2(s) =< 2 + 2s, 4 + 14s, 5s > 7- let L1 and L2 be the lines whose parametric equations are x-3 = v - 4 2 z-1 L1 4 x - 1 L2 y 3 z - 4 4 8. a- Determine whether the lines are parallel ,skew or intersecting b- The distance between the Lj and L2 . 8- A normal vector for the plane 4x – 2y + 7z – 11 = 0 is 9- The distance between the point ( 9,8,3) and the plane x+ y - 2z = 5 is ... 10- Calculate the distance from the point S( 3,7,-4) to the plane 6x – 3y + 2z = 0 Ans d=3 11- Find the point at which the line with parametric equations x = 3 + 4t, y = 5 – 2t, z = 4 + 7t intersects the plane 2x + 4y – z = 1 Ans p( 8,3,-1) |d1-d2| 12- Show that D = represnts the distance between the parallel planes Vaz+b2+c2 ax + by + cz + d1 = 0, ax + by + cz + d2 13- Find the eqation of the line that passes through A(1,2,1) and intersects the line x+1 y-2 z+1 at right angle 2 = and *"= =-11 intersect 15- Find the equation of that contains the line x-y+z=2, x+y+2z34 and the line 14- Show that the lines x-2 у+3 z+4 y-9 %3D 1 х-1 5-x 16- Find the equation of the plane that contains the line 2+y %3D 2 = 5 - z, and the point P( 0,5,2).
Transcribed Image Text:4- Find parametric and symmetric equations of the line passing through the points (1,- 1,2) and (2,1,5). 5- Find the distance from the point s(1,-6,2)to the line x = 2 + 3t, y = -4 + t,z = -2t Ans >>d=1.79 6- Find the distance between the skew lines defined by L1: r(t) =< 1+t,2 + 6t, 2t > L2: r2(s) =< 2 + 2s, 4 + 14s, 5s > 7- let L1 and L2 be the lines whose parametric equations are x-3 = v - 4 2 z-1 L1 4 x - 1 L2 y 3 z - 4 4 8. a- Determine whether the lines are parallel ,skew or intersecting b- The distance between the Lj and L2 . 8- A normal vector for the plane 4x – 2y + 7z – 11 = 0 is 9- The distance between the point ( 9,8,3) and the plane x+ y - 2z = 5 is ... 10- Calculate the distance from the point S( 3,7,-4) to the plane 6x – 3y + 2z = 0 Ans d=3 11- Find the point at which the line with parametric equations x = 3 + 4t, y = 5 – 2t, z = 4 + 7t intersects the plane 2x + 4y – z = 1 Ans p( 8,3,-1) |d1-d2| 12- Show that D = represnts the distance between the parallel planes Vaz+b2+c2 ax + by + cz + d1 = 0, ax + by + cz + d2 13- Find the eqation of the line that passes through A(1,2,1) and intersects the line x+1 y-2 z+1 at right angle 2 = and *"= =-11 intersect 15- Find the equation of that contains the line x-y+z=2, x+y+2z34 and the line 14- Show that the lines x-2 у+3 z+4 y-9 %3D 1 х-1 5-x 16- Find the equation of the plane that contains the line 2+y %3D 2 = 5 - z, and the point P( 0,5,2).
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