The line that is perpendicular to the lines r = ⟨4t, 1 + 2t, 3t⟩ and R = ⟨-1 + s, -7 + 2s, -12 + 3s), and passes through the point of intersection of the lines r and R

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

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

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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: Determine the intersection point of the two lines or show that they do not intersect. a. The line…

A: Given problem:- Determine the intersection point of the two lines or show that they do not…

Q: Show that the line joining the points P(0,1,2) and Q(3,4,8) is parallel to the line joining the…

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Q: For the line 2x + 3y = 6, find a line parallel to it containingthe point 11, - 12. Also find a line…

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Q: The three points (3,-5), (-a+2,3), and (2a+3,2) lie on the same line. What is a?

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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…

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Q: The slope of the line passing through the points (k, 1) and (5, -11) is perpendicular to the line 4x…

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Q: Show that the lines 2 x+3 y-1 and 6 x-12 y-1-0 are not perpendicular

A: As we know that, if the product of slope of two lines are (-1)  then both the both lines are…

Q: Find the value of z that makes lines u and v parallel. 6x-3 117 O -5

A: We know that when two lines are crossed by another line (called the Transversal), the pairs of…

Q: Determine whether the lines r1(t) = 〈0, 1, 1〉+ t〈1, 1, 2〉 and r2(s) = 〈2, 0, 3〉+ s〈1, 4,…

A: line1:xyzt1+t1+2t and line2:xyz2+s4s3+4sto find the point of intersection we need to equate both the…

Q: Determine the point of intersection of the lines. 4:[x, y, z]=[-3, 1, 4]+s[-1, 1, 4] (2:[x, y, z] =…

A: Let (a,b,c) denote the point of intersection So, For l1a=-3-s0b=1+s0c = 4+4s0For l2,a =…

Q: Determine whether the lines through the pairs of points are parallel A (2,3), B (2, -2) and C…

A: Slope of line passing through A(2,3) and B(2,-2) is:

Q: Determine whether the lines 5x+3y =9   and -3x+5y=10  are parallel, perpendicular, or neither.

A: We know that  Two lines with the same slope are parallel. Two lines whose slopes have a product of…

Q: Determine whether the lines L1 and L2 passing through the pairs of points are parallel,…

A: Slope is basically the vertical or the horizontal change between two distinct points. In a graph,…

Q: Determine the intersection of the lines: L,: ==4 and L2: x = y -1 = z

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Q: The line through (1,-3, 4) that is parallel to the line x- 3 + 4r,y= 5-1,2 = 7

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Q: Find the slope of the line that is a) parallel to the line containing (a, 0) and (0, b). b)…

A: Given the points (a,0) and (0,b). We need to find the slope of the line: 1) parallel to the line…

Q: Find the intersection point of the two lines: [x, y] = [1, 2] + t[2, -1] and [x, y] = [0, 3] + t[3,…

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Q: Which of the following is the point of intersection between the lines 3x + y = 10 and x - y = 2 а.…

A: Given:   3x + y = 10    x - y = 2

Q: Show that the lines 2 x+3 y-1 and 6 x-12 y-1=0 are not perpendicular

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Q: Prove that the equation 2x2-3xy-2y2-x+3y-1=0 represents a pair of perpendicular lines

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Q: Determine the point of intersection of the lines γ1 : ¯r1(t) = ⟨3, 2, 1⟩ + t⟨1, 0, 1⟩ and γ2 :…

A: First let's suppose both line are intersecting each other so, r1 = r2 then solve for t and s.

Q: If the line joining the two points (5,4)(5,4) and (3,−k)(3,−k) is parallel to the line kx−9y+11=0…

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

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Q: The intersection of plane A and plane S will be The intersection of lines n and k is W A x, Point X…

A: The intersection of two planes is a line. The intersection of 2 lines is a point The intersection of…

Q: Find the point of intersection, P, of the lines x - 3 y – 3 Z – 6 3 2 2 x – 2 y – 1 z – 7 - - - 4 4…

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Q: Determine whether the lines L1 and L2 passing through the pairs of points are parallel,…

A: We know that two lines are parallel if their slopes are equal. Also, two lines are perpendicular to…

Q: Which line is parallel to the line that passes through the points (1, 7) and (-3, 4)? OA ya-s 3 y =…

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Q: Find x such that the line through (3, -2) and (4, 7) is perpendicular to the line through (-2, 3)…

A: A detailed solution is given below

Q: Consider the two lines L1: x =-2t, y = 1+ 2t, z = 3t and L2: x =-9+5s, y = 5s, z = 4+ 2s Find the…

A: As the lines intersect thus their components are equal thus equate the components of the lines L1…

Q: Determine whether the lines L1: (0, −1), (5, 9) and L2: (0, 3), (4, 1) passing through the pairs of…

A: Given: Line L1 passes through 0, -1 and 5, 9.Line L2 passes through 0, 3 and 4, 1 To Find: To…

Q: Determine whether the lines through the pairs of points are perpendicular.  A (2,0), B (1, -2) and…

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Q: Determine whether the lines L1: (−2, −1) and L2: (1, 3), (5, −5) passing through the pairs of points…

A: Since, we have been given that two lines are L1: (-2,-1), (1,5) and L2: (1,3) , (5,-5). Our Aim is…

Q: Determine whether the lines (1,1,1)+ t(1,2,-1), and (3,2,1)+(-1,-5,3) are parallel, intersect, or…

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Q: The intersection of the lines x = a and y = b is the point (b, a). true or false

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Q: Which of the lines x – y + 3 = 0 and x – 4y –7= 0 is father from the origin? -

A: Consider the provided question, Hello. Since your question has multiple parts, we will solve first…

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: Show that the line joining the points P(0,1,2) and Q(3,4,8) is parallel to the line joining the…

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Q: What is the general equation of a line given the points P(1,3) and Q(4,7)? O 4x-3y+5=0. O 4x+5y+3=0…

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Q: . Determine if the lines are parallel, perpendicular, or neither. 2x+ 3y = 6 2 y =--x+4 **4

A: Equations of two lines are :- First line            2x + 3y = 6 Second line           y = (-2/3)x +…

Q: Show that the line joining the points P(0,1, 2) and Q(3, 4, 8) is parallel to the line joining the…

A: From the given problem:    L1:P0,1,2→x1,y1,z1Q3,4,8→x2,y2,z2   L2:R-2,32,-3→x1,y1,z1S52,6,6→x2,y2,z2…

Q: Determine whether the lines 2x + 5y =7 and 5x +2y =2 are perpendicular true or false

A: Compare the equations with standard equation  y=mx+c

Q: Show that the points A = (2, 5), B = (6, 1), and C = (8, - 1) lie on a line by using slopes.

A: The slope of a line is determined using any two distinct points on the line. The slope is calculated…

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A: Given :          The lines y = 2x - 1 and y = ax + 2 are perpendicular .   To find the value of a.

Q: Find b so that the points (4,-6), (5,-8), and (b,-2) lie on the line

A: Please find the solution in the attached images :

Q: Select all lines that are perpendicular to y -4 =- (r+1) O y = +8 O 3r 2u- 2

A: The given line is y-4=-23x+1 ............................ (1)  Compare with,

Q: Explain why the lines below intersect. l1: (x, y, z) = (2, 3, 4) + n(1, 2, – 3) and l2: (x, y, z) =…

A: Given : Vector equation of the line l1 : x, y, z=2, 3, 4+n1, 2, -3 Vector equation of the line l2 :…

Q: Determine whether or not the line through the points A(0, –4, 2) and B(5, –1, 0) is perpendicular to…

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