1. Find the distance between these lines L : [x, y, z] = [-2, 1, 1] + [3, 1, 1]; 1 € R L₂: [x, y, z)=[7,-4, 3] + s[−1, 1, 0]; s =R

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

A:

Q: a point Q(x2, y2) is on the line segment passing through R(-2,5) and S(4,1). Find the coordinates of…

A: Given: Given that the point Qx,y is on the line segment passing through R-2,5 and S4,1 Point Q is…

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: 18. Find the points of intersection of the lines 4₁: R= 2i + 3j + 3k + t(i-2j + 5k) y +1 2 12: x + 3…

A: These two line not intersect

Q: Let r¡(t) = (-4,0, –5) + t(0, 1, –3) and r2(s) = (2, –2, 10) + s(2,0, 3). Find the point of…

A:

Q: -. Find an equation of line L. (1,3) (-3, –1),

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

Q: r1(t) = (3, –6, 2) +t (-4, 2, –4) r2(t) = (-3, 3, – 10) + t (2, 1, 0) Find the point of…

A: Lines r1 and r2 can be rewritten as follows:

Q: Show that these two lines are coincident. L1: [x, y, z ] = [1, 5, − 2] + s [1, 7, − 3] L2: [x, y, z…

A:

Q: 2. For the following pair of equations, determine if they represent the same, parallel, or different…

A: The equation of the first line L1 is r=1, 0, 3+s3, -6, 3 and the second line L2 is r=2, -2, 5+t2,…

Q: Find the point of intersection of the lines x = t, y = -t + 2, z = t + 1, and x 2s + 2, y = s + 3, z…

A: we have to find the point of intersection of the given lines

Q: Find the distance between two parallel lines y = 2/3x +7 and -2x+3y=12

A:

Q: Determine if the following two lines are parallel, coincident or distinct: h:ri= (-5,-3, 1] + t (-3,…

A: The given lines are                          l1 : r1→=-5, -3, 1+t-3, 1, 0 ; t∈ℝ…

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: Which of the lines x – y + 3 = 0 and x – 4y –7= 0 is father from the origin? -

A: Consider the provided question, Hello. Since your question has multiple parts, we will solve first…

Q: Find the distance d between the points (1, 3) and (5, 6).

A: Our Aim is to find the distance between the points (1,3) and (5,6).

Q: Find the line of intersection between the lines: +1 and +.

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

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: Determine the distance between the point (8,-2,-1)and the line (x, y, z) = (-1,4,-3) + k(5,-4,-2),…

A:

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…

A: