Let L, be the line passing through the point P=(8, -6, 0) with direction vector a=-3, 3, 1]", and let L2 be the line passing through the point P2=(12, 11, -17) with direction vector đ=[-3, -1, -3]". Find the shortest distance d between these two lines, and find a point Q, on Lj and a point Q2 on L2 so that d(Q1.Q2) = d. Use the square root symbol V" where needed to give an exact value for your

Q: What is the horizontal of line through the point (4,-6)?

A: Solution: In the XY coordinate system, the point notation is always written as (x,y) And, x…

Q: The distance from the origin to the line passing through the points (0, 1,3) and (1,-1,2) is 14.

A:

Q: The distance between the line x =-2+2t ,y=2t+1, z=2-t and the line x=3-2t ,y=-2t+1 ,z=t is

A: We are supposed to find the distance between the line x =-2+2t ,y=2t+1, z=2-t and the line x=3-2t…

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: -2 + t,3 + 2t) and Qu (4 +

A: Solution: The objective is to what does the given lines have common.

Q: Find a set of symmetric equations for the line “A" perpendicular to the lines having direction…

A:

Q: Show that the line [3, 2, 3] passes through the point of intersection of the lines [2, 1, 1] and…

A: It has to be proved that the line 3,2,3 passes through the point of intersection of the lines 2,1,1…

Q: Let A be the point with coordinates (-3, 2, -1) and let B be the point with coordinates (2, 0, 0).…

A:

Q: Compute the distance from the point (3, 0, -1) to the line containing the points (1,0,−4) and (1,…

A:

Q: Let A be the point with coordinates (-3, -2, 3) and let B be the point with coordinates (2, 0, 0).…

A: To find the distance from point D to line l.

Q: Show that points A(5,2,-4), B(1,1,2), and C(-3,0,8) all lie on a straight line. Determine the…

A:

Q: Find the line perpendicular to y=2x-3 and through the point (2,-3) B) find the lines both parallel…

A:

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

A: let A be the point with coordinates 2,-1,0 and let B be the point with coordinates 2,0,0 let l be…

Q: Find the distance of the line segment that goes from (0,2) to (1,7)

A:

Q: Assume a line y = mx + c, [asses through the points (1, 15) and (-3, -5) Determine the slope, m, of…

A:

Q: Find the distance between the points (3, 8) and (-1, 11) and the slope of the line containing them.

A: We need to find the distance between (3, 8) and (-1, 11). Compute the distance between x1, y1, x2,…

Q: Find equations for the followingineF - The line through y and parallel to Z-axis

A: To find the equation of the line that passes through 1, 1, 1 and parallel to the z‐axis.

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.