3. A pair of lines in R³ are given. Determine whether they are parallel, intersecting or skew. If the lines intersect, find the point of intersection. a) r(t) = (2+4t, 6t, 4 – 2t) R(s) = (-2+ 2s,8+ 2s, 2 + 6s) z+2 b) L === 3

Q: Given: [x, y,z ] = [1,−1,5]+t [3,4,7], determine • the symmetric equations for the line • If…

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Q: Given directed line segment AB, where A(0,0) and B(6,0). Determine the point P that partitions the…

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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: Show that the pair of bisectors of the angles between the straight lines (ax+by)?=c(bx-ay)², c>0 are…

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Q: Consider lines L, and L,. L4: x = 1 + t, y = t, z = 8 + t, t ER, L2: x – 9 = y – 1 = z - 9 (a)…

A: We have to find whether the lines are parallel or not if they are parallel then find the shortest…

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

A: I have appended the formula used in the solution part of the question

Q: Let A= (1,2,4), B=(4,1,5), C=(4,2, 6), D=(7,1,7) Find the exact distance between the lines AB and…

A: I am going to solve the given problem by using some simple calculus to get the required result.

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 value of z that makes lines u and v parallel. 6x-3 117 O -5

A: We know that when two lines are crossed by another line (called the Transversal), the pairs of…

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: Determine whether the given lines are distinct parallel lines, coincident lines, intersecting lines,…

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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: Which of the following is the correct definition for perpendicular lines? O Lines that intersect and…

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Q: 1. Look at this diagram: R U If PR and SU are parallel lines and mPQO = 111°, what is mZRQT? Explain…

A: We have to find the value of m<RQT where PR↔ and SU↔ are parallel lines and m<PQO=111° We…

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

A: Let C be a piecewise smooth curve defined by, Let P and Q be two continuous functions of x and y…

Q: 8. Lines p and q are intersected by transversal t as shown. What value of x proves that linesp and q…

A: Follow the procedure given below.

Q: 1. Look at this diagram: Q R If PR and SU are parallel lines and MKPQO = 111° what is mz RQT?

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

A: Given that lines m and l are parallel.

Q: Which of the followings are false? I. L, : x = 1 +t, y= -2+ 3t, z = 4 – t and L2 : x = 2s, y = 3+ 8,…

A: We need to check whether lines interests or not

Q: 4. In this figure, lines a and b are intersected by line t.

A: Answer: ∠1 ≅∠3  .

Q: P2: Given two lines (zt+l, st-s. lot) ( 3+, ztr3, 2t+1) loca ted in side th plane plane, find 7.

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Q: 1. Which statement would not prove lines m and n parallel? 157° /h c/ g b/f a/e n. In the image, Zb…

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Q: Graph the line that satisfies each condition. 24. contains (–3, 4) and is parallel to AB with A(2,…

A: 24. At first we will calculate the line AB↔  Then,…

Q: Show that the pair of bisectors of the angles between the straight lines (ax+by)2=c(bx-ay)2, c>0 are…

A: TO  PROVE-  The pair of bisectors of the angles between the straight lines   (ax+ by)2 = c( bx-ay)2,…

Q: Use the figure below and the given information to determine if lines m and n parallel. Figure not…

A: Explanation and solutions is given below.....

Q: Three or more lines are _____ if theey all intersect at only one point a. Intersecting b. Parallelc.…

A: Three or more lines are concurrent if they all intersect at only one point.

Q: L1:x = 1+ 2t, L2:x = 2 – s, y = -1 - t, y = 3s, z = 3t, z = 1+ s, -00 <t< 0 -00 <t< 0

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Q: Suppose a line that appears parallel to side BC of ΔABC intersects sides AB and AC at points C and Y…

A: Suppose a line that appears parallel to side BC of ΔABC intersects sides AB and AC at points X and Y…

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: 3. Evaluate ryde where C is the line sogment from (0,1) to (2, 2).

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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: Two parallel lines are cut by a transversal as shown below. Suppose m Z8 = 48°. Find m Z1 and m Z3.…

A: We can use the concept of parallel lines in order to solve the given problem .

Q: If M(3, 10) is the midpoint of the line segment AB and if A has coordinates (−1, 2), find the…

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Q: I need help with this question

A: Determine whether the lines of symmetric equations are parallel, perpendicular or skew.

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: 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: If A(4,8,12), B(2,4,6), C(3,5,4) and D(5,8,5) are four points, show that the lines AB and CD…

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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: Consider the points a, b, c, d and the lines L, M in the following figure.

A: Given a graph containing the points a, b, c, d and lines L, M

Q: Which supplementary angles can prove that lines L and M are parallel? 3 4 5 6 7 8 M- A. 7 and 8 B. 4…

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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: Let l1,l2, l3 be three parallel lines and let t, and t2 be traversals intersecting these lines. Let…

A: As per given figure,  l1, l2, l3 are parallel, t1 and t2 will meet at some point O at some angle,…

Q: Suppose a line that appears parallel to side BC of △ABC intersects sides AB and AC at points X and Y…

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Q: If M(6,8) is the midpoint of the line segment AB and if A has coordinates (2,3), fınd the…

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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 M(4, –5) be the midpoint of a line segment joining two points A and B. If the coordinates of A…

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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: 46. If the lines a¡x + b¡y = c1 and a2x + b2y = c2 are %3D parallel, what can you say about the…

A: Topic:- parallel lines