ri(t) = (4.5, 6.5, 7.5) + t (1, 1, 1) r2(t) = (-9,5, 18)+ t (4,0, –4) Find the point of intersection, P, of the lines rį and r2. P =

Q: find the distance d between the points P1 and P2. P1 = ( - 0.2, 0.3); P2 = (2.3, 1.1)

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Q: Find a plane containing the point (6,-7,7) and the line x(t) y(t) z(t) = = = - 2 - 6t - 1 + 5t 5-t

A: Here we have to find the equation of plane

Q: 2:- find the line of interSection o f the plane -2x + 73 - 2324 given by 3x t6y-52=-3 f the plane

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Q: In the accompanying diagram, trans- versal RS intersects parallel lines +> XY and WZ at E and H,…

A: Given: RS is transversal line that means it intersects two parallel lines (XY and WZ). Therefore…

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: – 2x + 4y -dA, where R is the parallelogram enclosed by the lines 5y Find - r - R - 2x + 4y = 0, –…

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Q: Show that r1(t) and r2(t) define the same line, wherer1(t) = t (2, 1, 3), r2(t) = (−6, −3, −9) + t…

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Q: Determine whether the lines r1(t) = 〈0, 1, 1〉+ t〈1, 1, 2〉 and r2(s) = 〈2, 0, 3〉+ s〈1, 4,…

A: line1:xyzt1+t1+2t and line2:xyz2+s4s3+4sto find the point of intersection we need to equate both the…

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: Ex(29):- Determine whether the line and the plane are intersect; if so, find the point of the…

A: Given, The equation of the line   L : x=t, y = t, z =t  Equation of the Plane : PL : 3x-2y+z-5=0…

Q: Show that |R²| = |R| by doing the following.  Show that "a square is an interval" and "a plane is a…

A:

Q: Find an equation of the plane containing the lines L1 and L2 in R3 L1: x = t ; y = -t ; z = t L2:…

A: We have to find equation of plane containg Line L1 and L2  -

Q: F = (-3y, 3x); R is the triangle with vertices (0, 0), (1, 0), and (0, 2).

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Q: Determine B such that the line 3x +2y – 7 = 0 is perpendicular to 2х- Ву+2%3D0. O A. 5 О В.4 С. 3 O…

A: Let m1 and m2  be the slopes of the lines L1 and L 2 . If  L1 is perpendicular to L 2  then m1×m2 =…

Q: Ux the fact that х у 1 a b 1-0 a b 1 to deiermine the equation of the line passing through the…

A: Let (x,y) be a point on the line connecting the points Now if  they are on the same line, the area…

Q: 116 (14x+18) Find the value of x for which the lines p and q are parallel. O A) 8 B) 6 O C) 9 O D) 7

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

A:

Q: and Lg:글3D%3D- z+3 Q4] Find distance between lines L1: =5

A: solution:-L1 : x-13 = y-22= z+32L2 : x-22 = y+2-1= z-34distance between two line is given by L1 :…

Q: Q8) The distance between the line x=-1+t, y3D3+2t, z=-t and the plane 2x-2y-2z=3 is: *

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: 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: Let the point A = (-1,3,-3 ) be the lines r:X=(1,1,-2)+t(2,-1,2) te R a) The distance between the…

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Q: Find a plane containing the point (-3,-3,5) and the line x(t) y(t) z(t) = = 8 + 4t -4-6t -7-3t

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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…

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Q: Use the result in Exercise 21 to find the equation of the line that contains (5, – 1) and is…

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Q: 6x Find -dA, where R is the parallelogram enclosed by the lines 4x – 3y 6x – y = 0, 6x – y = 9, – 4x…

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Q: 4x + 5y Find dA, where R is the parallelogram enclosed by the lines -x-2y 0, 4x + 5y 4, --2y 1, --2y…

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Q: Find the point P' symmetric of the point P(-5, 13) with respect to the line 2x - 3y - 3 = 0

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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: 30. The slope of line / in the standard (x, y) plane is . Which of the following is an equation of a…

A: Givenslope of line l=m1=23To calculate: which line is perpendicular to line l.concept: Two lines are…

Q: -62-y Find dA, where R is the parallelogram enclosed by the lines -3x +y R - 6x – y = 0, - 6x – y =…

A:

Q: HER Verify that the two lines are parallel, and find the distance between the lines. (Round your…

A: Given

Q: Q2) a.) Find the intersection coordinates of lines passing from AC and BD. +x 17.42 BO--- -165.05…

A: Two lines intersects at a point where and coordinates of both the lines is same. Equation of line…

Q: ind the point of intersection for the lines v(t) = (-5, - 8, -6)t + (− 1, 3, 1) and (u) = (6, 6, 2)u…

A: First we find value of parameters u and t .

Q: Determine the intersection point of the two lines or show that they do not intersect. a. Does the…

A: Please see the answer below.

Q: Let F = x i+ (x + y) j+ (x - y + z) k. Let the line I be a = 3t – 4, y = 3t – 3, z = 2t – 2.

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Q: Use the result in Exercise 21 to find the equation of the line that contains (4, 5) and is…

A: Given- 2x+3y=6 To find- The equation of the line which is passing through the point 4,5 and…

Q: ind an equation of the line of intersection of the following two plane x + y + z = 0 nd 2я — у + 32…

A: We have to find out

Q: Determine whether the lines Lj and L2 are parallel. L: x = 1– 2t, y = 4 + t, z = 6 – t L2: x = 4 –…

A: L1:x-1-2=y-41 =z-6-1=tdirection ratio: V1=(-2, 1, -1)L2:x-4-6=y+23 =z-7-3=tdirection ratio: V2=(-6,…

Q: about the line, x- | (E'1) puo (!!)'(0) squiad %3D V= T RG) 3-X y= 2x+1 Idy 3 - 23. x- V= T 29 12

A:

Q: 2x + 4y Find -dA, where R is the parallelogram enclosed by the lines - x – 5y – 2x + 4y = 0, – 2x +…

A: given integral ∫∫R-2x+4y-x-5ydA where R is the parallelogram enclosed by the lines…

Q: 4. Determine the intersection of lines:L,:= = and Lz X=Y-1=2 11 >\J

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Q: Evaluate A dr where C is the line joining (0, 0, 0) and (2, 1, 1), given A= (2y + 3)I +xj+(yz – x)k.…

A: # given A=(2y+3)I+xzj+(yz-x)k  Then to find integral(A*dr) from (0,0,0)to(2,1,1)

Q: Q2) A- Find the distance between the line (y = x + 3 ) and center of circle (x²+y²–2x=0).

A: Topic : Coordinate Geometry  Answer  question no 2 :- sqrt(8) As per our guidelines,  at a time only…

Q: 4x бу Find dA, where R is the parallelogram enclosed by the lines 6x + 2y 0, 4x R 4х — бу - 6y = 4,…

A: Evaluate the double integral by change of variables

Q: Use the result in Exercise 20 to find the equation of the line that contains (4, 5) and is parallel…

A: We know the important theorem is that the graph of Ax+By=C is parallel to the graph of Ax+By=D.…

Q: Consider the points P(1,0,3) and Q(5, 2, -1), and the line 1: { x = -7-2t y=t z = 9+t

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Q: Find the point (if it exists) at which the following plane and line intersect. y = - 10; r(t) = (4t…

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