Prove that, if the rays that bisect a pair of alternate interior angles are parallel, then the lines are parallel

Q: 2. Find the volume of the parallelepiped having a = (1,4,–7), b = (2,–1,4) and c = (0,-9,18) as…

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Q: If L is a line through 0 and if ŷ is the orthogonal projection of y onto L, then || ŷ|| gives the…

A: To state whether the given statement is true or false :  By definition, we know that, if L is a line…

Q: Show that the vector v = ai + bj is perpendicular to the line ax + by = c by establishing that the…

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Q: If 0 is the acute angle between the planes x + y = 2 and x + y +2z = 6, then 2cos (e) = O 1 O 1 O 2…

A: Given equation of planes are x+y-2=0 and x+y+2z-6=0 Let Let A1 x + B1 y + C1z + D1 = 0 and A2x + B2y…

Q: Suppose P,Q,R,S are four collinear points such that: a. Q is between P and R. b. Ris between Q and…

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Q: Let j = and i = Compute the distance from j to the line through u and the 9. origin.

A: Given that y→=-39 and u→=12. To find the distance from y→ to the line through u→ and the origin, we…

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Q: In general, show that the vectors V = ai + bj and W = -bi +aj are always perpen-dicular. Assume a…

A: Given vectors are v=ai+bj and w=-bi+aj, where a≠0 ,b≠0. We know that two vectors are perpendicular…

Q: Let θ be the angle between the line y = mx +b and the x-axis. Prove that         m = tan θ.

A: The slope of a line is the rate of change of the y-axis with respect to x. Formula for slope=riserun…

Q: Q. OS bisects LPQT If m/PQS = 3x + 13 and MLSQT = 6x – 2, find m/RQT.

A: Since, Line QS bisects  ∠PQT, So, it means that QS divides  ∠PQT in two equal angles such that:…

Q: Suppose that u and v are vectors in R7 both of length 2√2 and that the length of u - v is also²√².…

A: Solution :

Q: ) Four non-coplanar points A, B, C, D are positioned such that the line AB is perpe ular to CD, and…

A: In this question, the concept of the dot product is applied. Dot Product The product of the…

Q: what is the parametric and symmetric eqvotions of the line that passes thrs point (4.-3,57 to beth…

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Q: When do directed line segments in the plane represent the same vector?

A: Vectors are represented by the line segments in which the length of the line segment is called the…

Q: On parable y=x^2/2 set point, which distance from point P=(4,1) is minimal.

A: Given: Equation of parabola: y=x2 /2                      point P= (4,1) To find: Point on parabola:…

Q: Suppose L1 and L2 are disjoint (nonintersecting) nonparallel lines. Is it possible for a nonzero…

A: Given:

Q: Forces are called concurrent when their lines of action meet in Perpendicular planes Select one:…

A: Given the statement Forces are called concurrent when their lines of action meet in perpendicular…

Q: Show that except in degenerate cases, (u * v) * w lies in the plane of u and v, whereas u * (v * w)…

A: We will prove that  (u*v)*w=(u.w)v-(v.w)u u*v=ijkuxuyuzvxvyvz…

Q: What is the angle between 2a + 3y + z = 5 and x – ay + az = 7?

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Q: Solve for the projection of the vector P = (3,4, 4) onto Q = (0, –2, –5). What is the exact measure…

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Q: IfL is a line through 0 and if ŷ is the orthogonal projection of y onto L, then || ŷ||l gives the…

A: The given statement is "If L is a line through 0 and if y^ is the orthogonal projection of y onto L,…

Q: If two planes are not parallel then the in a

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Q: Suppose di ,de,..do ore distinct real numbecs det Prove ė lineerle fade pendent ere vectors in…

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Q: let v = (1, 3, −2) and w = (2, −1, 4).  Compute the angle between v and w

A: Given: v = (1, 3,−2) and w=(2,−1,4).

Q: What part is needed to prove the triangeis are congruent by SAS?

A: Choose the correct option.

Q: By vector methods, show that the line segment joining the midpoints of two sides of a triangle is…

A: To prove :- The line segment joining the midpoints of two sides of a triangle is parallel to the…

Q: Suppose that u and v are vectors in R7 both of length 2 /2 and that the length of u - v is also2 /2.…

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Q: Show that the vector v = ai + bj is perpendicular to the line

A: GivenVector V = ai + bj and the line ax + by + c

Q: If L is a line through 0 and if f is the orthogonal projection of y onto L, then || F|| gives the…

A: Option B is correct.

Q: () - Does vector T = belong to Span (S), where

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Q: Use vectors to prove that the line connecting the midpoints of two sides of a triangle is parallel…

A: Let the arbitrary triangle has vertices A, B and C has three vectors AB, →AC →  and  BC → . Let M…

Q: Prove that all the points on a perpendicular bisector of a line segment AB are equidistant from the…

A: Statement:All the points on a perpendicular bisector of a line segment AB are equidistant from the…

Q: Which of the vectors OP = (1,-1,5) and og = (2,-1,0) is not perpendicular to the line Li- - z.…

A: The equation of a line that passes through the point x0 , y0 , z0 in three dimensional space is…

Q: Suppose that Tui, Tus As lineady independent (Here, TELLU, W)) Prove that vi, Vz is linearly…

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Q: State the difference between a position veetor and a line vector.

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Q: From Be helie angle, ZA- No ma 9=ZAt Zる 2.comp Module ma ZA= 4 Vto Z8 Lt ZA k 2-55 ZB cosp

A: Yes it is possible. Multiply and divide the numerator of right hand side of equation by ZB. Given…

Q: If DE is not parallel to FG, what is DE? 23 F DE = [ %3D Submit

A: topic - isosceles trapezoid  non parallel sides of isosceles trapezoid are equal

Q: Which of the letters B, O, K, I, V, F, X, D, L, and Y are their own images under a rotation by an…

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Q: Let abcd be a rectangle. the perpendicular bisector of line segment bd intersect ab and bc in point…

A: Given that ABCD be a rectangle, the perpendicular bisector of line segment BD intersect AB and BC in…

Q: 3. Prove Theorem 3.5 by completing each direction of the biconditional as given sepa- rately in the…

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Q: Use a directed line segment to represent the vector.u = (2, −4)

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Q: Find the angle of least positive measure(in degrees, not equal to the given measure) that is…

A: To find the least positive coterminal of A=471°

Q: Find the angle of least positive measure (in degrees, not equal to the given measure) that is…

A: The coterminal angle is the angle that is obtained by adding and subtracting from the given angle.…

Q: Prove that of all triangles having two given sides of lengths a and b, the one whose sides form a…

A: It is given that the length of two sides of a triangle is a and b, respectively. It is known that…

Q: Use vectors to prove that the line joining the midpoints of two sides of a triangle is parallel to…

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Q: Suppose that u and v are vectors in R? both of length 2/2 and that the length of u-v is also2 2.…

A: We will use expansion of u-v to find the angle

Q: Compute : fr (Re z – 3z) dz where r is a directed line segment from z = 0 to z = i .

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Q: show that if ||u||=||v||, and u and v are not parallel, then u+v and u-v are perpendicular.

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Q: Use a directed line segment to represent the vector.u = (−3, −4)

A: The directed  line segment is the vector drawn from the any two points in the cartesian plane. The…