24. Consider the lines l: x = Xo +tv and m: x = x1 + su. Show that l and m intersect if and only if xo – Xị lies in Span (u, v).

Q: Evaluate the line integral 6ydx + 4xdy where C is the straight line path from (2, 3) to (5, 5). Jc…

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Q: show.. that the line in.which. the planes.X+zy-223D5 and. 5X-zy.-7=D0.jntersect.is. pavalle.to. the…

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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: (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: Find paromet ric aquation of Line L where to paiut A(Xmiya) is and

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Q: 4. Prove that the midpoint of the line segment connect- ing the points (x 1, X 2, - . . , Xp) and…

A: The midpoint of a segment can be considered to be the average…

Q: If there were no understood restriction to lines in a plane in Theorem 1.4.3, the theorem would be…

A: The given statement is " In space, there is exactly one line perpendicular to a given line at any…

Q: Prove the converse to theorem 2.6.2 let l and m be  two lines. If there exists a unique point P…

A: Solution:→                  Let Assume;                        Lines are not distinct.…

Q: Evaluate the line integral 4ydx + 2xdy where C is the straight line path from (4, 2) to (8, 4).…

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Q: Consider these lines, where s,t, E R 11: [x, y, z] = [2, 1, -4] + t[1, 3, 1] 12: [x, y, z] = [1, k,…

A: Two lines are said to be coplanar if they lies in same plane. The equation of line passing through…

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

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Q: Let 1, y E R². Show that p:=y is the closest point on the line Span(y) to z.

A: Given, x,y ∈ R2 To show: p=x.yy.yy is the closest point on the line span y to x

Q: Write an indirect proof in paragraph form.

A: Given: m∠1≠m∠2

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

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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: If v = (1,2 ) draw all vectors w = (x, y) in the xy plane with v · w = x+ 2 y = 5. Why do those w's…

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Q: Find the plane through P = (4, −1, 9) containing the line r(t) =〈1, 4, −3〉+ t〈2, 1, 1〉.

A: The plane contains the line r(t)=1, 4, -3+ t2, 1, 1, so a vector in the plane is 2, 1, 1. The line…

Q: d s: X = (0,1, -1) + λ (1, α, 2α) are coplanar, in which case study its relative position.

A: Consider the given lines. r: X=(1,0,2)+λ (2, 1, 3) And, s:X=(0,1, -1)+λ(1, α, 2α) Let r and s are…

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

A: Given that lines m and l are parallel.

Q: Determine the way in which the line [x, y, z] = [2,−3, 0] + k[−1,3,−1] intersects the plane[x, y, z]…

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

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

A: For first line L1, the line passes via origin, i.e., 000 and the line is parallel to u=110, so, the…

Q: 3. Show that the lines L :1 = 2+t, y = 2+3t, 2 = 3+t and La :1 = 2+t, y = 3+ 4t, 2 = 4+ 2t…

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Q: 3) Consider the line L in R? spanned byp = (6). Let PL(u) be the orthogonal %3D projection of the u…

A: b = 4

Q: Determine the way in which the line [x, y, z] = [5, −9, 3] + k[1, −12, 2] intersects the plane [x,…

A: Determine the way in which the line [x, y, z] = [5, −9, 3] + k[1, −12, 2] intersects the plane [x,…

Q: If l,, l2, and l3 are nonconcurrent lines, prove that there exist three points. Exactly one each…

A: Three or more points are said Lto be collinear if they all lie on the same straight line If l1 , l2…

Q: 9. Are the lines parallel, perpendicular or neither. Show work. 4. y3-x+2 3 3x+4y = 4 %3D

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Q: Find the Polnt otintersectton of the lines: l,: x = 2+t, y =3+2t,z z 4 +3t X = S+ 2, y= 2S+4, 2=…

A: Here we will find the point of intersection of given lines,

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: Compute x2z ds where Cis the line segment from (0,6,-1) to (4,1,5). 7 6 .A O 56 .B O 16/77 .c O 56 3…

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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: Consider points A, B, C, and D, no three of which are collin- ear. Using two points at a time (such…

A: Given information: A, B, C and D are four points in which no three points are collinear.…

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: C. Show that the lines with symmetric equations (x y z) and (x+1 are skew, and find the distance…

A: L1 ;  x=y=z     x-01 =y-01=z-01  x1=0    y1=0     z1=0α1=1    β1=1      γ1=1L2:  x+1=y2=z3…

Q: How is the line y = 1 converted by mapping w = e? ?

A: In this question, we convert the line y=1 by mapping w=e^z.

Q: Y Find S Zdz Such that c is the line which joining A,B,C and D as follows A (o,1) yB (2,1) , C…

A: Here, firstly we have draw the line C with the given points. Then we have to find integration value…

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

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Q: Compute x2z ds where Cis the line segment from (0,6,-1) to (4,1,5). 7 6 .A O 56 77.B 16/77 .c O 56 3…

A: The line segment is from 4,1,5 to 0,6,-1 . Hence, this line is parallel to the vector, 4,1,5-0,6,-1…

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: 13. XPOQY and AOB are straight lines. PO =0Q and 21 = L2. Prove that ZA = ZB. B. A

A: That's easy. Have a great day!!!

Q: Show that the line in which the planes x + 2y – 2z = 5 and 5x – 2y - z = 0 %3D intersect is parallel…

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

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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: 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: Given ∡ 2 + ∡ 3 = 180°∡ 2 + ∡ 3 = 180°, which theorem proves the lines r and s parallel.

A: If two parallel lines are cut by a transversal, then same side interior angles are supplementary.…

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: 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.