For what values of the constants k and c does the line x- 3 ** =- lie in the plane x - y + 2z = c? O A. k = -2, c = 0 O B. k = -8, c = 2 O C.k = -10, c = 1 O D. k = 10, c = -1 O E. k = 10, c = 0

Q: Find k so that the line through (4, -1) and (k, 2) is a. parallel to 2x + 3y = 6, b. perpendicular…

A: The line passes through the points (4, -1) and (k, 2). Then the slope (m) of this line is: m = [2 -…

Q: Is there a value for k that would make the line between the points (k,2) and (3,8) horizontal? If so…

A:

Q: 22. Find the distance from the point (5, 2, -1) to the line х — 1 - 2 1 3

A: Given equation of line is, x-12=y1=z3 The point is Q(5,2,-1).

Q: Find the length of the perpendicular from (2,-3) to the line 2x - y +9 = 0?

A:

Q: Which of the fallowing lines are parallel to line ur(3,0,1,5.2) O (3,0,-1,5, 2) O (6.0,-2,-10,4) O…

A: If we multiply any number to vector that are parallel vector

Q: Find the coordinates of the point which divides the line segment connecting (-1,4) and (2,-3) into…

A:

Q: Show that the lines 2 x+3 y-1 and 6 x-12 y-1-0 are not perpendicular

A: As we know that, if the product of slope of two lines are (-1)  then both the both lines are…

Q: 2. Passes through (3, 5) and (-1, 5) 3 4. Perpendicular to the line y=--x-7 2 and passes through…

A: Given points (3,5) and (-1,5) Therefore slope m = (y2-y1)/(x2-x1) m = (5-5)/(-1-3) = 0 Therefore…

Q: The line through (1, 2, 3) that is perpendicular to the lines x = 3 - 2t, y = 5 + 8t, z = 7 - 4t and…

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: . Which of the following lines passes through the point (2, 5)? y = 2z – 1 y = 2z +1 y = 4z -2 y =…

A:

Q: How Find the pistance from fant(,3). and Line y -4

A: on solving that we get d=1

Q: Find the point of intersection of the lines: y = 4x + 1 and y = -2x +4 %3D o (2,9) 으(4,2) ㅇ (4,3) O…

A:

Q: Show that the perpendicular let fall from any points on the straight line 7x - 9y + 10 = 0 upon the…

A: See the details solution in below

Q: Find the point on the line T = (-2, 2, 3) + t(4, 1, 1) that presents the shortest distance to the…

A:

Q: 2 What is the equation of the line perpendicular to y– 3=-(x+3) and has an x-intercept of 6? A 2…

A: topic - equation of a line perpendicular to given line and with x intercept

Q: What is the equation of the line that passes through the points (4, –7.5) and (6, –3.5)? - 1 x – 5.5…

A:

Q: Find K so that the line through( 1, 5 )and( K, 8) is a) parallel to 4y -3X =7 and b) perpendicular…

A: compute the equation of a line joining (1,5) and (k,8) by using below formula.

Q: 22. Find the distance from the point (5, 2, –1) to the line x – 1 2. || ||

A: A line in three-dimensional geometry can be represented by parametric form, vector form, or…

Q: Find the point of intersection, P, of the lines x - 3 y – 3 Z – 6 3 2 2 x – 2 y – 1 z – 7 - - - 4 4…

A:

Q: How far is the intersection of the lines 4x-5y=26 and 3x+7y+2=0 from the origin

A: We have to find the distance of the intersection of the lines 4x-5y=26 and 3x+7y+2=0 from the…

Q: The area bounded by the curve y=4x y=4x  and the lines x=6x=6 ,x=10x=10 and x−axisx−axis is: Choose…

A:

Q: The two points on the lines 2x +3y +4 = 0, which are at a distance of 2 from the line 3x + 4 y –- 6…

A:

Q: that

A:

Q: Compute x2z ds where Cis the line segment from (0,6,-1) to (4,1,5). 7 6 .A O 56 .B O 16/77 .c O 56 3…

A:

Q: Find the equation of the Mane that contains the line 3X - 2:2 = - 39 = 7-7 and that is Para llel to…

A: When the plane is parallel to the line x-y+z=2: Here n1→=i^-j^+k^ and a→=2i^+3j^+k^ To find…

Q: * Let LIEX-54+10=D0 L2=4X+y-1-O be two lines. 1 Show that the lines L and Lz are not parallel.

A:

Q: Two straight lines 3x - 2y + 5 = 0 and 6x - 4y + 10 = 0 intersect at the origin. are coincident. are…

A: This question is based on straight line intersection.

Q: The distance from the point (5, 3) to the line 2x + 4y + 5 = 0 is O 2.457 O 3.801 O 4.63 O 6.037

A:

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: + y = 9 that is closest to the point (−5,

A: The line is: 6x+y=9 Point (-5,3)

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: Compute x2z ds where Cis the line segment from (0,6,-1) to (4,1,5). 7 6 .A O 56 77.B 16/77 .c O 56 3…

A: The line segment is from 4,1,5 to 0,6,-1 . Hence, this line is parallel to the vector, 4,1,5-0,6,-1…

Q: The two points on the lines 2x + 3y +4 = 0, which are at a distance of 2 from the line 3x +4 y – 6 =…

A:

Q: Which is a subset of a line with one endpoint and extends infinitely in one direction?

A: A ray is a subset of a line that has only one endpoint and extends infinitely in one direction  If…

Q: Find the point of intersection of the lines r;(t) = (-1, 1) + t(8, 4) and rɔ(s) = (2, 1) + s(8, 6)…

A: Consider the given lines in polar form. To find the intersection points equate the x and y…

Q: What is the point at which the lines x = 3 - t, y = 2 + t, z = 5t intersects with x - y + 2z = 9 ? О…

A:

Q: 9. Solve for x and y that make the lines parallel.

A:

Q: Evaluate (x + y) ds, where Cl is the line segment from (-2, 1, –5) to (-1, –1, –2).|

A:

Q: What is the equation of the line that is parallel to the line y = -¼x + 5 and passing th point (2,…

A:

Q: Is the line that contains the points P1(−3, 1) and P2(1, 3) perpendicular to the line that…

A: We can check the line joining the points are perpendicular or not as per the concepts as below.

Q: Suppose that L is a line through the points (a, 2, c) and (3, –4, 2) that is parallel to one of the…

A: Given that: L is a line passing through (a,2,c) and (3, -4, 2) and parallel to one of the axes.

Q: The line through (8, 5) that is parallel to 3i+2j. Ox = 8+51, y = 3+2t Ox = 8+81, y = 5+5t Ox =…

A: Given query is to find the equation of the line.

Q: Find the distance between the line through A(4, 0, 2) and B(2, 4, 1) and the line through C(1, 3, 2)…

A: Find the distance between the line through A(4, 0, 2) and B(2, 4, 1) and the line through C(1, 3, 2)…

Q: How far is the point (2, -3) from the line 3x - 4y +7 =0? O 5 O 4 O 6 O 7

A:

Q: Let l: = = -: - 5 and p = (1,7, -4) + A(1, -2, 2) be two lines in space.

A:

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.