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 linex = 2 + 3t, y = -4 + t,z = -2tAns >>d=1.796- Find the distance between the skew lines defined byL1: 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 arex-3= v - 42z-1L14x - 1L2y3z - 448.a- Determine whether the lines are parallel ,skew or intersectingb- The distance between the Lj and L2 .8- A normal vector for the plane 4x – 2y + 7z – 11 = 0 is9- 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 = 0Ans d=311- Find the point at which the line with parametric equationsx = 3 + 4t, y = 5 – 2t, z = 4 + 7t intersects the plane 2x + 4y – z = 1Ans p( 8,3,-1)|d1-d2|12- Show that D =represnts the distance between the parallel planesVaz+b2+c2ax + by + cz + d1 = 0, ax + by + cz + d213- Find the eqation of the line that passes through A(1,2,1) and intersects the linex+1y-2z+1at right angle2= and *"= =-11 intersect15- Find the equation of that contains the line x-y+z=2, x+y+2z34 and the line14- Show that the linesx-2у+3z+4y-9%3D1х-15-x16- Find the equation of the plane that contains the line2+y%3D2 = 5 - z, and thepoint P( 0,5,2).

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Answered: 4- Find parametric and symmetric…

Math

Calculus

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

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 21E

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Question

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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