1. The lines 4: x=1-t, y=2+t, z=-2-t; 12:x=3+s, y=-1+s, z = 2s are skew.

Q: Compute ye*ds where Cis the line segment from (1,2) to (4,7). .A 16 34 e4

A: According to the given information, it is required to calculate the value of integral.

Q: Compute ye" ds where C is the line segment from (1, 2) to (4, 7).

A: We have to compute ∫Cyexds where C is the line segment from 1,2 to 4,7. We have, x-14-1=y-27-2=t

Q: 2. Evaluate S. 3x – 6y ds for C is the line segment from (6,0) to (6,6).

A: Solution

Q: For what values of a are the points (6, 2, 3) and (a, 2, 5) and the line r = (2,−1, −2) + t(3,1, −2)…

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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: 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: 13. In AMNP, if mZM = 4x - 3, mZN = 9x-6, and m/P = 6x-1, find x and the measure of each angle. %3D…

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Q: 17. For what value(s) of k, if any, will the lines *+1_y+2 3 k 7=(6,−1,0)+t(6,1−k,2) perpendicular?…

A: Product of DRs of two perpendicular lines is 0

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: Compute yds ds where C is the line segment from (1, 2) to (4, 7).

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Q: Compute ff, x²ydA,where Dis the triangle bounded by x = 2, y = 1, y = 1 –

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Q: lem 17. What multiple of a = (1,1,1) is closest to the point b= (2,4,4)? Find also the poin st to a…

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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: 4. The vertices are at (7,-5) and (7,1) and the length of the transverse axis is 10.

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Q: 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…

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Q: Let C be the line segment connecting the points P(−2,1,−4) and Q(5,−4,3). Evaluate ∫C(2x+4z)dy…

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Q: Sc 7ydx + 3z dy where C is the straight line path from (2, 4) to (4, 7).

A: The parametric equation of the straight line between the points (a,b), (c,d) is x-ac-a=y-bd-b=t,…

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: The equation of the line segment from A(3, – 4,4) to B(5,2,5), 0<t<1 is a. r= (3+ 2t)i +(- 4+6t)j+(4…

A: Topic = vector  correct option 'a'

Q: Evaluate ry dr + r'dy, where C is the rectangle with vertices (0,0), (3,0), (3,1), and (0,1)

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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: Find a parallel line that passes through the given p (3, 4), y = 2x - 7 O y = 2x +2 O y= 1/2x + 2 O…

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Q: Consider a crowded beach where the population of beach-goers is uniformly distributed across its…

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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: Find the stundand matices * and a for ToT,OT and て:→ド,1)- (-3y, fn + 3) T:→ド, 1.(4)): (J,)

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Q: Suppose that two lines Re((1+i)z+2i+3) = 0 and Re(2-bi)z+5) = 0 are perpendicular. then b=.

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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: -> 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: 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: 2- The line perpendicular to the triangular (PQR) and through the point (P) if P(1,-1,2), Q(0,3,1),…

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Q: In a plane, if line f is perpendicular to line m and then fln. mln f || n n || f m || n

A: In the question we have to choose correct option.

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: 7) through: (-5, 5), perp. to y=x- 4 8) through: (3, 4), perp. to y =-2x- 4 9) through: (4, 4),…

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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: Compute yds where C is the line segment from (1, 2) to (4, 7).

A: We know that,       . Now,

Q: If JK = 11 and MK = 21 and MJ = 10, which point is in between the other two? %3D

A: 4) We have given JK=11 and MK=21 and MJ=10To find which point is in between the other two.

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: 16. If the lines y = 3x + 1 and 2y = x + 3 are equally inclined to the line y = mx + 4. Find the…

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

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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: 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: 13. Determine the distance between the following lines. [x, y, z]= [4,5,9]+s[-3,4,-9] and [x, y, z]=…

A: Above question is solved.

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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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.