Let l: = = -: - 5 and p = (1,7, -4) + A(1, -2, 2) be two lines in space.

Q: Find b such that (2, -1), (3, 2), and (b, 5) lie on a line.

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Q: Let I be the line (1, -1, 1) + t(0, 2, 1). Let Q = (1,0, 1). Find the distance from Q to l. distance

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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: What are the directing cosines of the line whose symmetric is (x + 2)/ - 1= (y-3)/ 2 = (z + 4)/ 6

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Q: Determine the value(s) of k such that the lines 2y= -kx +6 and 3y-x= 2kx+3  are perpindicular.

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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: Which of the following lines is perpendicular to the line   y  =  1/2x + 1   and contains the…

A: Consider the given line y=12x+1                                … 1

Q: Which is the equation of a line that has a slooe of 4 and passes through point (1, 6)? O y- 4x - 2…

A: Given Line passing through 1,6 slopem=4

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

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

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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: Show that these two lines are coincident. L1: [x, y, z ] = [1, 5, − 2] + s [1, 7, − 3] L2: [x, y, z…

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Q: Let L, be the line through the origin and the point (5, 0, –1). Let L, be the line through the…

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Q: Show that the perpendicular let fall from any points on the straight line 7x - 9y + 10 = 0 upon the…

A: See the details solution in below

Q: Let I be the line (1, -1,1) + t(0, 2, 1). Let Q = (1,0, 1). Find the distance from Q to l. %3D

A: Given line is                                                       l:1, -1, 1+t0, 2, 1 vector…

Q: Find the point of intersection of the lines r(t) = (1, 0, 0) + t(-7, 3, 0) and s(t) = (0, 1, 1) +…

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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: Let L7 be the line passing through the points Q1=(-5, -5,-3) and Q2=(-1,-3, 3) and let L2 be the…

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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: Do the lines (x, y, z) = (5 + 2t, 3 + 2t, 1 - If not, how do you know? t) and (x, y, z) = (13 – 3r,…

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

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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 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: Show that -ydx+xdy) = x₁y₂-₂₁ where C is the line segment joining (x,y) and (x₂,₂).

A: We have to prove ∫C-ydx+xdy=x1y2-x2y1 Where C is the line segment joining x1,y1 and x2,y2 Now…

Q: Let L, be the line passing through the point P1=(-1, -2, -2) with direction vector d-[-3, -3, 1]",…

A: L1 is the line passing through the point P1(-1 , -2, -2) with direction vectord→ = -3, -3, 1Tand L2…

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.

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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 the exact distance between lines l1: 7 = (5,–3,7) + s(3,-2, 5) and l2: 7 = (2,-7,9) +…

A: Here both the lines are parallel.

Q: 10. Show that these two lines are coincident. [x, y, z]= [1, 5, -2]+s[1, 7, -3] [x, y, z]=[-3, -23,…

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Q: Construct a line parallel to a given line through a given external point. * R A

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Q: In triangular space it is sufficient to know two different points to find the line passing through…

A: Given statement is 'True'

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: There are 8 points in a plane, and no three points are collinear. These 8 points, taken 2 at a time,…

A: Combination: The possible number of ways to select r items from the total n items is given by:…

Q: Find the distance between lines x + 3y = 5 and x + 3y = 25.

A: The distance between two parallel lines can be calculated using the formula,

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: Which is a subset of a line with one endpoint and extends infinitely in one direction?

A: A ray is a subset of a line that has only one endpoint and extends infinitely in one direction  If…

Q: Find the point of intersection of the lines r;(t) = (-1, 1) + t(8, 4) and rɔ(s) = (2, 1) + s(8, 6)…

A: Consider the given lines in polar form. To find the intersection points equate the x and y…

Q: show.. that. the line in.which. and. .5Xm2y.Z==.0. jntersect..is

A: Equation of the plane: - In three-dimensional space, a plane surface is represented by an equation…

Q: Evaluate (x + y) ds, where Cl is the line segment from (-2, 1, –5) to (-1, –1, –2).|

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

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Q: standard form of the line with center (5,1) and tangent to the line 7x+2y=17

A: Given Data: Center: (x1, y1) = (5, 1) Tangent: 7x+2y=17   The general equation of tangent is,…

Q: nd the point of intersection of the lines: = 4x + 1 and y = -2x + 4 1,2) 1,2) 2,9) ,3)

A: All points of intersection satisfy both curve(lines) .  Hence , for point of intersection  We equate…

Q: If C is the straight line from (1,1,1) to (2,1,2) find 2xlnzdx + 2y²zdy + y³dz.

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Q: Let I be the line (1, -1, 1) + t(0, 2, 1). Let Q = (1,0, 1). Find the distance from Q to l.

A: In a 3 dimensional space, a point and a line can be at infinite number of distance from each other,…

Q: Find the equation of the line that satisfies the given conditons.  Through (-6,-7); perpeindicular…

A: Given: line passing through (-6, -7), perpendicular to line passing through (-3,5), (1,3).