3. If A, B, C and C' are constants, show that:(a) the lines:Ax + By + C = 0Ax + By + C`= 0are parallel

Answered: Image /qna-images/answer/70e26e52-401a-48fb-bb87-a7be3ea6440f.jpg

Answered: If A, B, C and C`are constants, show…

Math

Calculus

If A, B, C and C`are constants, show that: (a) the lines: Ах + By + C%3 0 Ах + By + C' 3 0 are parallel

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section1.1: The Coordinate Plane

Problem 3E: The distance between the points (a, b) and (c, d) is ___________. So the distance between (1, 2) and...

See similar textbooks

Related questions

Q: Verify that the two lines are parallel and find the distance between the lines. L1: x = 2 − t, y…

Q: Q10)The two lines L1: x=3-2t, y=4+t ,z= 6-t and L2: x=5-4t, .y=-2+2t, z=7-2t are parallel

A: 10) The equation of the line x=3-2t t=x-3-2 y=4+t t=y-4 z=6-t t=z-6-1

Q: Which equation represents a line that is parallel to 2y = 6x - 4 and passes through the point (-1,…

A: as per bartleby guidelines we are supposed to solve only one question

Q: Find a and b such that the lines r1 = (1, 2, 1) + t(1, −1, 1)andr2 = (3, −1, 1) + t(a, b, −2) are…

A: Given: r1=1,2,1+t1,-1,1 r2=3,-1,1+ta,b,-2 r1 and r2are parallel only if a1=b-1=-21

Q: (B.) Determined by the intersecting lines L1 and L2 L1 : {x = 2t, y= 4- t, z = 3 +t}and L2:{x = 2 +…

A: According to guidelines we solve one question. thanku.

Q: 1. Show that the lines having the equations 4x- 3y + 12 = 0 and 8x 6y + 15 = 0 are parallel.

Q: Verify that the lines are parallel, and find the distance between them L1: x = 2 - t, y= 3 + 4t, z =…

Q: Show that the lines having the equations 4x – 3y + 12 = 0 and 8x – 6y + 15 = 0 are parallel.

A: According to question,Given equation of lines,4x - 3y +12 = 08x - 6y +15 =0

Q: Consider two lines: l1(t)=⟨6+4t, 8−2t, 2+6t⟩ & l2(t)=⟨1+4t,3−2t,4+5t⟩ a) Do they intersect? If…

Q: Suppose the symmetric equations of lines l1 and l2 are = 2 – y = z and x = -1, 2 3 espectively.

Q: 11a) Are the two lines parallel? Show work 4 (3, 2) -30] 2. (5,-1) 【け1.-B12 2

A: Given: Co-ordinates of line l1=(-3,0) and (3,2) Co-ordinates of line l2=(-1,-3) and (5,-1)

Q: Determine the symmetric equations of line that passes through the points B and С.

Q: 8 What is the slope of the line perpendicular to tne line represented by the equation 2x+4y = 12?…

Q: 9) 7x+4 60° 1.

A: The figure is given by To evaluate: The value of x

Q: Find the equation of the line through point (3,7,-11) y is perpendicular to the xz-plane

Q: Show that the lines whose direction cosines are given by l+m+n=0,2mn+3nl-5lm=0 are perpendicular to…

Q: 2) Determine whether the lines 1: x = 1+ 2t, y = 3t, z = 2 – t and l2 : x = -1+ s, y = 4 + s, z…

Q: 1. Find the angle between the lines L,:x = 3 + 8t, y = -6t,z = –7+ 24t and L2:x = 3 + 8t, y = 15t, z…

A: Solving only ques 1 according to guidelines.

Q: find value(s) of k so that the lines described by 3x = 2y+11 and kx = 40 - 6y are perpendicular

Q: 4. Determine the intersection of lines:L = aund LzX= とz 11 >\J

Q: Find the point of intersection of the lines x = t, y = -t + 2, z = t + 1, and x 2s + 2, y = s + 3, z…

A: we have to find the point of intersection of the given lines

Q: 3- The line jaining the origin and Point_of intersection of the linesr(X=l+2t_ ys-3+4Ł,2=t) aul (x-…

A: Given that: Lines are: L1: (x=1+2t, y=-3+4t, z=t) and L2: (x=-2+3t, y=-5+3t, z=-12+34t)

Q: find the distance between the Linel L) through A(I,0,-1), B (-1,)andthe Line (L2) through C…

Q: You have three lines: LI: x = 3 + 2s, y = -1+4s, z 2-s L2: x = 3+ 2t, y 2 +t, z=-2+ 2t L3: x = 1+ 4u…

Q: Find x'z ds, where C is the line segment from (0,2,-3) to (6,0,-6) C

A: To find:∫Cx2z dsThe line segment is from 0, 2, -3 to 6, 0, -6

Q: Suppose L, is the line through the origin in the direction of u and L2 is the line through the point…

A: We are given two lines L1 and L2 in 3d, and we have to find the closest points x1 , x2 such that the…

Q: * Let LIEX-54+10=D0 L2=4X+y-1-O be two lines. 1 Show that the lines L and Lz are not parallel.

Q: Which of the following lines is perpendicular to the line y  =  12x + 1 and contains the point…

A: Given line is y=12x+1 And the point is (2, -2) By comparing the equation of line y=12x+1 with…

Q: (1) What is the relationship between the lines L1 and L2? where L:x = 1-t, y = 4 + t, z = 2+3t L2:x…

Q: 20. Consider lines €1 and l2. l1 : [x, y] = [1, 4] + [[-7, 2] l2 : [x, y] = [-2, 6] + t[k, 9] a) For…

A: We know that two lines are parallel if their slope are equal and perpendicular if the product of…

Q: Determine if the lines ℓ1: x − 9 = −t, y + 4 = 3t, z − 9 = 3t and ℓ2: x − 1 = s, y − 4 = −s, z − 9…

Q: D F OF and GI are parallel lines and mZDEH = 116°, %3D Submit

A: DF and GI are parallel line,

Q: 12- Show that the lines L1 and L2 are parallel and also find the distance between them. L1: x=2-t,…

A: Solution: Consider the given lines in parametric form; L1:Consider x = 2 - t = x0+ aty = 2t = y0 +…

Q: For the line €: (x, y, z) = (5, - 3, 2) + n(1, 2, - 2), find a) a point of the line. b) a direction…

A: Given parametric equation of line - x, y, z = 5,-3, 2+n1, 2,-2x, y, z = 5,-3, 2+1n, 2n,-2nx, y, z =…

Q: 1. Show that the lines 2x + 3y = 1 and 6x - 4y - 1 0 are perpendicular.

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Construct perpendicular lines from point P to line m. 1. VE

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the other…

Q: Find xz ds, where C is the line segment from (0,-2,4) to (0,-6,1).

Q: 8. Find a line uniquely parallel to the line 3x-4y+12=0.

Q: 1. Find the angle between the lines L1:x = 3 + 8t, y = -6t, z = -7 + 24t and L2:x = 3 + 8t, y = 15t,…

Q: For the line €: (x, y, z) = (2, 3, 4) + n(3, - 2, 5), find a) a point of the line. b) a direction…

A: the given line is: l:x,y,z=2,3,4+n3,-2,5 we have to find: (a) a point of the line. (b) a direction…

Q: Find the equaation of the pair of lines intersecting ar (2,-1) parallel to the pair 6x2-13xy-5y2=0

Q: is this true or false......When lines m and n intersect at point P , it follows that m ∩ n…

A: This is true: in Euclidean geometry/plane. if two lines m,n intersect at a point P ,then m…

Q: Show the lines (x, y, z) = (5 + 2t, 3 + 2t, 1 – t) and (x, y, z) = (13 – 3r, 13 + 2r, 4 + 4r) are…

A: Given:- Show the lines (x, y, z) = (5 + 2t, 3+2t, 1- t) and (x, y, z)= (13-3r, 13 + 2r, 4 + 4r) are…

Q: suppose I tell you that the line ax+5y=7 is parallel to the line 4x-2y=11. What is a?

A: Given equation of the line 4x -2y = 11 .......(1)and another line 9x+5y = 7 .....(2)we find the…

Q: Show that the equation of the line in R' through distinct points (1, Y1) and (x2, Y2) can be written…

A: We have to show that the equation of the line in R2 through distinct points x1,y1 and x2,y2 can be…

Q: The distance between the line x =-2+2t ,y=2t+1, z=2-t and the line x=3- 2t ,y=-2t+1,z=t is

A: Distance between two Parallel Lines we calculate as a distance between intersection of the lines and…

Q: Suppose that the two lines ay= x-y and 2/ax+3y=1 are parallel. What must be the value for a?

A: First of all, consider general equation for the straight line. Also consider the given equations.

Concept explainers

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.

Question

3. If A, B, C and C' are constants, show that:
(a) the lines:
Ax + By + C = 0
Ax + By + C`= 0
are parallel

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Cartesian Coordinates$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions

Line l is parallel to plane P that is, it will not intersect P even if extended. Line m intersects line l.What can you conclude about m and P?
The distance between the points (a, b) and (c, d) is ___________. So the distance between (1, 2) and (7, 10) is __________ .
Prove that if two lines neither horizontal nor vertical are perpendicular, then the product of their slopes is -1. HINT: See Figure 10.19. You need to show and use the fact that ABC~EDC.
Show the lines (x, y, z) = (5 + 2t, 3 + 2t, 1 − t) and (x, y, z) = (13 − 3r, 13 + 2r, 4 + 4r) are not parallel, and that they do not intersect. Such lines are called skew.
is this true or false......When lines m and n intersect at point P , it follows that m ∩ n = P
Show that the product of the perpendicular distances from the origin to the pair of straight lines represented by ax2+2hxy+by2+2gx+2fy+c=0 is
A new line is formed from a point (2,−3) to a line y=−4x−12. What is the perpendicular distance from the given point to the original line?
Suppose a line that appears parallel to side BC of ΔABC intersects sides AB and AC at points C and Y respectively, and AX/AB=1/2. How can you determine if the line is or is not parallel to BC? Explain.