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: a. 7 = (3, 1) + (-3, 5), te R b. x = -6 + 2s and y = 3 - 2s, se R Two lines L₁ = (5, 3) + p(-4, 7),…

A: The given lines are:L1​:  r=⟨5,3⟩+p⟨−4,7⟩,    p∈RL2​:  r=⟨5,3⟩+q⟨2,1⟩,    q∈R Both lines intersect…

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: 28. In the standard (x, y) coordinate plane, the point (2,-6) is the midpoint of the line segment…

A: Given,  In the standard x,y coordinate planeThe point  2,-6  is the midpoint of the line segmentwith…

Q: Do the points (0.5, 1), (1, 1.2), (2, 2) lie on a line?

A: Three points will lie on same line if slope of any two point is same as other two points, taken two…

Q: 1. The line y - 6 = 2(x + 4) passes through which point? OA (-4,-6) O B. (4, −6) Oc( 4, 6) OD (2,6)

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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: 2. Sketch the line = (-4,-4) + t(6,8).

A: To sketch the line r=(-4,-4)+t(6,8)

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: Find the distance between each pair of points: a) (0, - 3) and (4, 0) c) (3, 2) and (5, - 2) b) (-2,…

A: Distance between two points x1, y1  and x2, y2 is  d = x1 - x22 + y1-y22  a) (0, -3) and (4, 0) d =…

Q: Let A be the point with coordinates (-2, -1, -1) and let B be the point with coordinates (2, 0, 0).…

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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: The intersection point of the line y = +2 and the x-axis is

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

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Q: Find the value of X such that and are perpendicular

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Q: Determine the angle between the lines AB and AC delimited by the points A(4,3,2), B(6,1,-2),…

A: Step 1:  Step 2: Step 3: Step 4:

Q: Determine the exact distance between lines l1: 7 = (5,–3,7) + s(3,-2, 5) and l2: 7 = (2,-7,9) +…

A: Here both the lines are parallel.

Q: 3. Find the best values of a, and a, if the line y=a₁x+a is fitted to the d (0,1),(2,5), (5,12),…

A: this is question  of geometry  here line equation  is given  and point are given we have to find…

Q: Find the point of intersection of the two lines l1 : 7 Intersection point:

A: Introduction: The point of intersection is the intersection of two lines or curves. A point is the…

Q: H.w.. Find the distance from the point (2,12)andthe Line

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Q: Determine if the lines ℓ1: x − 9 = −t, y + 4 = 3t, z − 9 = 3t and ℓ2: x − 1 = s, y − 4 = −s, z − 9…

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Q: If a line passing through (-4,3) cuts off the smallest area from the second quadrant in a coordinate…

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