Find the distance between the parallel lines in each pair. a) l₁: [x, y, z] = [2, 5, 4] + [2, 1, 3] l₂: [x, y, z] = [-4, 0, 1] + s[2, 1, 3] b) l₁: [x, y, z] = [5, 3, -2] + [4, -5, 2] l₂: [x, y, z] = [-7, 1, 1] + s[4, -5, 2]

Q: Find b such that (2, -1), (3, 2), and (b, 5) lie on a line.

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Q: 8. Find the point (x. y) such that (1, 3) is the midpoint of the line segment connecting a. (x, y)…

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Q: Find the point on the line x - 3y+9 = 0 that is closest to the point (-1, 3). 1) (-0.9, 2.7) O 2)…

A: Closest distance form a point to a line is normal distance from point to line.

Q: et L1 be the line that passes through (2, 1,0) in the direction of (1, -1,2) and L2 be the line that…

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Q: Find the point at which the given lines intersect: r = + t r = + s

A: I think the equation of the first line is Thus, the parametric equations of two lines are x = 3 +…

Q: QR is located at Q(-5, -8) and R(-1, 3). Which pair of points would form a segment congruent to QR ?…

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Q: determine if the two lines are parallel, orthogonal or neither. n) The line by i=(4– 7t,-10+5t,21–…

A: Given

Q: Find x such that the line through (2, - 3) and (3, 2) is perpendicular to the line through (- 2, 4)…

A: We have the points A(2,-3),B(3,2),C(-2,4) and D(x,-1) We have to find the value of x such that the…

Q: The points (x, -5) and (2, y) are on the line containing the points (-14, 7) and (10, 1). What is…

A: equation of line containing two points (x1,x2) and (y1,y2) is y-y1=y2-y1x2-x1x-x1

Q: 1. Write the line parallel to y = -2x + 5 that passes through the point (1,1). a. y = -2x + 1 b. y…

A: Question 1 - The equation of line is given as - y = -2x + 5 Comparing the above line with the…

Q: Find the point where the two lines +s and +t intersect, if it exists

A: We need to find point where lines intersect.

Q: Match each line with a perpendicular line. A. y = 5x +2 1. the line through (2, 12) and (17, 9) В.…

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Q: Find B if A is (-4,7) and the midpoint of the line segment AB is (0,1)

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Q: The line that is perpendicular to the lines r = ⟨4t, 1 + 2t, 3t⟩ and R = ⟨-1 + s, -7 + 2s, -12 +…

A: The given lines r→=j^+t4i^+2j^+3k^R→=-i^-7j^-12k^+si^+2j^+3k^ Let,  4i^+2j^+3k^=b1→i^+2j^+3k^=b2→ As…

Q: Determine the midpoint of the line segment between A and B shown below: 2 -3 -2 -1 1 2 3 -1 -2 - -3…

A: It can be observed that the point A is and the point B is . According to the Midpoint formula, the…

Q: . Which three points are on the line L: r = (2,-5)+s(2,1), s € R? a. Q(2,1), 0(6,-3), R(2,-5) b.…

A: Explanation of the answer is as follows

Q: Find the slopes of the lines containing: a) (2, – 3) and (4, 5) b) (3, – 2) and (3, 7) c) (1, – 1)…

A: We know that slopem of line which contain two pointsx1,y1,x2,y2 is given by m=y2-y1x2-x1…

Q: Determine whether the lines (1,1,1)+ t(1,2,-1), and (3,2,1)+(-1,-5,3) are parallel, intersect, or…

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Q: a.) (-3,4); parallel to y=3x-5 b.) (-2,-4); perpendicular to y 2/3x-5

A: (a).   The given equation of line: y=3x-5 Slope of line parallel to the given line is: m=3

Q: 7. Find the distance from the point A to the line through the points B and C where A, B, and C have…

A:

Q: 25. Determine the x- and y-intercepts. a) [x, y] = [2, –4] + t[3, –1] b) [x, y] = [-8, 11] + t[5, 2]…

A: The given equations are in parametric form. To find x-intercept put y=0 and get the value of…

Q: Set 5. (-3, 4) and (2, 6) A. (2, 8) and (-3, 2) t. 11. (-5, -7) and (1, -2) G. (0, 1) and (-6, -2)…

A: As per guidelines we can solve only three subparts at a time so the first three subparts from left…

Q: Find the values of x and y that make the red lines parallel and the blue lines parallel

A: we have to find angle x and y  from the following figure.