What is the nature of the Intersection of the lines: X=1+3k y 5+2k. kER and 7 (4,7,-1) + t(3,2,-1), tER 7 = (4,7,-1) + 1(3,2,-1), tER z=-1k Select one: o a plane a point a line no intersection

Q: Q10)The two lines L1: x=3-2t, y=4+t ,z= 6-t and L2: x=5-4t, .y=-2+2t, z=7-2t are parallel

A: 10) The equation of the line x=3-2t t=x-3-2 y=4+t t=y-4 z=6-t t=z-6-1

Q: Determine if the line intersects the plane. If so, state the solution. [x, y, z ] = [− 1, − 9, 16]+t…

A: The given line is [ x, y , z] = [ -1, -9, 16]  +  t   [ 3, 3, -5]  and the given plane is x+4y+3z=11…

Q: Find a and b such that the lines r1 = (1, 2, 1) + t(1, −1, 1)andr2 = (3, −1, 1) + t(a, b, −2) are…

A: Given: r1=1,2,1+t1,-1,1 r2=3,-1,1+ta,b,-2 r1 and r2are parallel only if a1=b-1=-21

Q: 6. Find the intersection of the line / and the plane . 1:7=(4,-1,4) +t(5,-2,3) x: 2x+5y+z+2=0

A: Given is the equation of line as l:r→=(4,-1,4)+t(5,-2,3) Equation of plane as π: 2x+5y+z+2=0 First…

Q: 04: Find the distance between the parllel lines L, and L2 where L1: x = 2 - t, y = 2t, z = 1+t L2: x…

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Q: Which of the following is the equation of the plane that is pas the point P(2, 2,–2) and vertical to…

A: Given, the equation of the plane that is passing through the point   P(2, 2,-2) and vertical to the…

Q: Find symmetric equations for the line of intersection of the planes. 2 3x - y - 7, 2- Sx + 2y - 8 O…

A: Given:- Planes 1 z= 3x-y-z-7 Plane 2 z=5x+2y-8 To find:- Find symmetric equations for the line of…

Q: 5. (a) Find an equation for the line of intersection between the planes r+3y-z = 2 and 2x – y+2z =…

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Q: 3-Find the coordinates of the point on the line y= 3x+i. that is equidistance from (0,0) and (-3,4)…

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Q: Find a line passing through (−2, 5, −3) and perpendicular to the plane 2x − 3y + 4z + 7 = 0.

A: we have to find a line passing through (-2,5,-3) and perpendicular to the plane 2x-3y+4z+7=0   as we…

Q: Find the line of intersection of the given planes. 4x + y-z = 0 and 2x - y + 3z 4 %3D

A:

Q: (a) Find an equation for the line of intersection between the planes x+3y–z= 2 and 2x –y+2z = 5. (b)…

A: Given: Two planes  x+3y-z=2vector a = <1 , 3 , -1 >2x-y+2z=5vector b = <2 , -1 , 2 >

Q: Q8) The distance between the line x=-1+t, y=3+2t, z=-t and the plane 2x- 2y-2z=3 is: * 5 -units V12…

A: In a three dimensional picture, the line and plane are drawn as per their equations. It is desired…

Q: 11. Find x and y, then find g. Lines m, n, andpare parallel. 12 60° in 6 /y x° Select one: a. z =…

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Q: Find the plane through P = (4, −1, 9) containing the line r(t) =〈1, 4, −3〉+ t〈2, 1, 1〉.

A: The plane contains the line r(t)=1, 4, -3+ t2, 1, 1, so a vector in the plane is 2, 1, 1. The line…

Q: Determine the way in which the line [x, y, z] = [2,−3, 0] + k[−1,3,−1] intersects the plane[x, y, z]…

A:

Q: b) Determine, showing steps, whether the line [x, y, z] = []+¹] intersects the plane: 3 x + 7y + 8z…

A: We have to find the intersection of plane and line.

Q: 30 0= +시 +씨 2 |and 3x-y-z=3 -8/

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Q: Find the point of intersection of the lines r(t) = (1, 0, 0) + t(-7, 3, 0) and s(t) = (0, 1, 1) +…

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Q: Find the equ. nf line through the Pont (-2,3,4) and Parallel to Planes: 2X+3y +42=5 3X + 4Y+52=6…

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Q: Suppose the symmetric equations of lines l1 and l2 are = 2 - y = z and r = -1, 3 respectively. (a)…

A: If two lines are neither intersecting nor parallel then they are know as skew lines  If vector form…

Q: Determine the point of intersection of the lines γ1 : ¯r1(t) = ⟨3, 2, 1⟩ + t⟨1, 0, 1⟩ and γ2 :…

A: First let's suppose both line are intersecting each other so, r1 = r2 then solve for t and s.

Q: The plane that passes through  (9, 0, −3)  and contains the line  x = 6 − 3t, y = 2 + 5t, z = 4 +…

A: Given : A point (9,0,-3) where the plane passes through.             A system of equations for line…

Q: Q4:Show if the line (x = 5y +17, y+z-2= 0) lies in the plane 3x-41y-26z +1 = 0 or no ? Where does…

A:

Q: Find an equation for the plane that contains the line v = (-3,4,5) + t(3, 2, 4) and is perpendicular…

A: Given that: Equation of line: v=(-3, 4, 5)+t(3, 2, 4)Equation of plane: 2x+y-3z+4=0

Q: Find a plane containing the lines x = 3+ 21 x =1- 21 y = 4– 31 and y = 7+41 where -o <t<00, z =1-31.…

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Q: Find the point of intersection of the line through (1, -4, 1) and (4, -10, 5), and the plane given…

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Q: 9. In the standard (x, y) coordinate plane, line e contains the points (3, 5) and (5,8) and line m…

A: We have to find out k

Q: iven the points A(2,6,0) and B(3,5,6) determine the point of intersection of this line to x-z plane.

A: Given points are A(2,6,0) and B(3,5,6) The line joining points (x1, y1, z1) and (x2, y2, z2) have…

Q: Let r1(t)=⟨3,−6,−16⟩+t⟨0,−4,−4⟩ and r2(s)=⟨−9,2,−20⟩+s⟨−4,0,−4⟩. Find the point of intersection, P,…

A: We need to find point of intersection.

Q: Determine the way in which the line [x, y, z] = [5, −9, 3] + k[1, −12, 2] intersects the plane [x,…

A: Determine the way in which the line [x, y, z] = [5, −9, 3] + k[1, −12, 2] intersects the plane [x,…

Q: 12 Which point is equidistant from the planes T1:- 2x +y- 2z + 3 = 0 and 73: - 2x + y- 2z + 21 = 0?…

A: Option B is correct :- (explained below)

Q: The planes x - 2y + 4z - 3 = 0 and 2x - y - z + 3 = 0 are perpendicular. Select one: True False

A:

Q: Explain why the lines below are parallel. l: (x, y, z) = (2, 3, 4) + n(1, 2, - 3) and (2: (x, y, z)…

A: l1 : x, y, z=2, 3, 4+n1, 2, -3l2 : x, y, z=3, 7, -2+r-1, -2, 3 Here, The direction ratios of l1 are…

Q: 1. Determine the intersection (if any) of the lines I1: (x, y, z) = (2,0, 9) + s(1, 2, 3), s e R,…

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Q: Find general point for the lines The line through (0, -7, 0) perpendicular to the plane x + 2y + 2z…

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Q: 6. Determine the line of intersection of the planes X+2y +7z= 4 X+3y+3z = 1

A:

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: 3. What is the distance from the line to the plane? 7-(2,3,8)+(1.1.1) 2x - 5y + 32 + 10

A:

Q: Consider the line y = Bo + Bjx. (i) Let (x), y1) and (x, y2) be two points on the line. Show that…

A: Introduction: The regression equation for a simple linear regression model of the response variable,…

Q: Let fx) = 4 + x. (a) Estimate the ares under the graph of f, the x-axis, and the lines x = -1 and x…

A: As you have asked more than three subparts, i am answering first three subparts only as…

Q: 7. If the following lines intersect, determine the point of intersection. Otherwise classify the…

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Q: Find a plane containing the point ( - 5, - 5, 2) and the line r(t) = (1, - 2, 1) + t(4, 7, 5).

A: First you will find the normal vector to the plane and then find the value of the constant d

Q: 3) Determine the point(s) of intersection of the lines L₁: (3,1,5) + s(4,-1,2) and L₂: x = 4 + 13t,…

A: Given

Q: 6. Determine the line of intersection of the planes. X+2y +7z= 4 X+3y+3z =1

A: We use vector product to directional vector in which line of intersection of planes lies

Q: Explain why the lines below intersect. l1: (x, y, z) = (2, 3, 4) + n(1, 2, – 3) and l2: (x, y, z) =…

A: Given : Vector equation of the line l1 : x, y, z=2, 3, 4+n1, 2, -3 Vector equation of the line l2 :…

Q: Given the lines L1 and L2: L1: (x,Y.z)=(-4,6,-2)+t(5,4,3), with tER. www L2:…

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Q: Check the alternative that contains the points of intersection of the line r below with the…

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Q: 4:x 3+6r, y =-2+9t,: =1-12t and L:x=-1+4t, y 3+6,-8r

A: We are given L1: x=3+6t, y=-2+9t, z=1-12t. So, L1: x-36=y+29=z-1-12. Thus, a1=6, b1=9, c1=-12. We…

Q: 25. Find the intersection of the line [x, y, 2] = [1,4, – 2] + 1(1, – 1,3] and the plane 2r – 4y +…

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.