Show that the lines of equations x=−1+t , y=−2+t, z=3t for t∈R and x=5+s, y=−8+2s, z=7s for ?∈ℝ are skew. (Two lines in ℝ3  are skew if they do not intersect with each other and they are not parallel to each other).

Q: If the straight lines ax+by+c=0, bx+xy+a=0, cx+ay+b=0 are concurrent, then prove a'+b³+c³=3abc

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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: Given the lines l1 and l2; l1 :x = 1+ 3t, y = 2 - 6t, z = 7t – 3, x - 4 l2 : 6 - y 3 (a) Show that 4…

A: Answer

Q: Find the distance between the following skew lines  x/2 =y−46, z=0 x-1/2 = y/2 =z+3

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Q: Let line L: x = 2t, y = 0, z = 3, and let line M: x = 0, y = 8 + s, z = 7+s, for some constants t…

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Q: Prove that given lines are skew. L1: [x, y, z] = [1, 3, 7] + t[–1, 1, 2] L2: [x, y, z] = [4, –2,…

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Q: Consider the following four lines, given in either symmetric or ... form. Use them to answer…

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Q: Find the distance between the skew lines: x = 9+ 6t, y = 5 + 6t, z = 7 – 6t y = 7, x = 7 – t, z = 6…

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

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Q: 44. Select the pair of lines that are parallel. O 5x – 2y = -1 y = 4x – 1 4x – 6y = 6 2x – 3y = -6 -…

A: two parallel lines is of the form  ax+by=c and ax+by=d where a,b,c,d are constants

Q: Wishing to prove that / and m are skew lines. John began an indirect proofby supposing that / and m…

A: Given that l and m are skew lines.  Skew lines mean the lines which do not have the same slope,…

Q: Given the lines li and le: li8a = 1+も」 y = -2 -t, z = 3 -2t, l2: 2-2 y+ 1 3-Z - 3 skewed. 1) S how…

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Q: If the straight lines ax + by + c=0, bx + cy+ a=0,x+ay+b =0 are concurrent, then prove that a +b+c'…

A: Given straight lines,  ax + by + c = 0 bx + cy + a = 0 cx + ay + b =0 The three straight lines are…

Q: 3. Show that the lines L1 : x = 2+t, y= 2+3t, z = 3+t and L2:1 = 2+t, y= 3+ 4t, z = 4 + 2t…

A: L1: x =2+t , y= 2+3t , z= 3+t  L2: x =2+t , y= 3+4t , z= 3+t

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

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Q: B. H. If BF || DG and BF 1 BD, then BD [?] DG. to neither, they are skew lines

A: The solution is given below in the next step:@

Q: The distance between the following two skew lines is Line#1: [x, y, z] = [1, 1, 9] + t[1, –3, 0]…

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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: What value of x would prove that lines /and m are parallel?

A: Given that lines m and l are parallel.

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: Find the shortest distance between the skewed lines. l1: = 1+ 2t, y = -1+t, z = 2+ 4t and l2: x= -2+…

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Q: Find the distance between the skew lines: x = 4+ 9t, x = 4 – t, y = 3+ 2t, z = 7 – 4t y = 9, z = 8+…

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Q: Consider the skew lines: rị(s) = (s+1, –2s+2, –s+3) r2(t) = (-t, 2t, 3t +2) Find the distance…

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Q: 2. the live in IR and haring Passing through He oryin as it's divechor vecter intersects the line…

A: The line in IR3 passing through the origin and having 1u3 as it's direction vector intersects the…

Q: Which of the following represents two lines that are coplanar and do not intersect?

A: We want to find the lines which are coplanar and don't intersect.

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: The equations [2, 1, 6] + t[6, 1, 4] and [4, 1, 3] + s[2, 10, 9] Are parallel Intersect at one point…

A: Topic = Lines Given lines are skew lines.

Q: Determine if the following lines are intersecting, parallel, or skew. Line 1: x=1, y = 21+1, z = 31…

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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: 1. Determine if the following lines are parallel, intersecting, or skew a) x= 4 +5t b) y = -2t c) z…

A: Given:  a) x=4+5tb) y=-2tc) z=1+3td) x=10s, y=6+4s, z=4+6s

Q: -> For the two lines; ri(t) = [2,4, 3] + t(0,0, 2] and r2 (s) = [5, –1,0] + s[0, –3, 0], the…

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Q: Show that the two lines X= 2+ St J= 4 - 36 Z: 5+t X= 1+4t and y= 5-4t Z: -1+ SE skew Rind the…

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Q: Question 5. , Which of the following statements is true about the lines L1 : x= 4 – 2t, y = 2+ 2t, z…

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Q: 10. In the standard (x, y) coordinate plane, line r contains the points (6, 5) and (b,-5), and line…

A: Given problem is :

Q: 5. Find the point of intersection of the following lines x = 4t +2, y = 3, z = -t +2 b. x = 2s +6, y…

A: Given query is to find the point of intersection of line a and line b.

Q: Determine whether the lines L, and L, are parallel, skew, or intersecting. х — 1 y - 2 z - 12 %3D 1…

A: Given problem :-     To find:-  Intersection point of given lines

Q: Show that the two lines X= 1+4t X = 2 + St and y= 5-4t J= 4 - 36 Z: -1+ SE 2: 5+t Rind the distance…

A: There are two equations of line:

Q: Find k so that the line through (3, 2) and (k, 3) is a. parallel to 25x + 17y = 34, b. perpendicular…

A: We will be using the following concepts: Parallel lines have the same slope. The product of slope…

Q: Find the distance between the skew lines r(t)=⟨3,−2,−4⟩t+⟨−4,−2,5⟩ and p(s)=⟨5,2,1⟩s+⟨−6,4,7⟩

A: Given r(t)=⟨3,−2,−4⟩t+⟨−4,−2,5⟩ and p(s)=⟨5,2,1⟩s+⟨−6,4,7⟩

Q: Which of the following lines is perpendicular to the equa y=-2x + 8 Ox+2y = 8 O x- 2y = 6 O 2x-y = 1…

A: Perpendicular line

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

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Q: Which of the following represents two lines that are coplanar and do not intersect? (A Perpendicular…

A: Given that Two line that are coplanar and do not intersect

Q: What can you conclude if you know that the point (p, q) lies on the line y — тх + b?

A: The given equation of the line is, y=mx+b If a point lies on the line then the point satisfies the…

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

A: To show that the given two lines are skew lines. The two lines are                          l1 = (-2…

Q: Show that the lines px + qy + r = 0 and P1x + q1y +r¡ = 0 are parallel or identical if and only if…

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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: 1. Find the angle between the lines L1:x = 3 + 4t, y = 2 – 3t, z = 12t and L2:x = 8t, y = 2 – 15t, z…

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