Intersecting Lines: Consider the two lines given by: L1 : (x, y, z) = (3 – 5t, 7 + 2t, 4 – t), and L2 : (x, y, z) = (7+3s, 5 – s, 10 – 2s). Show L1 and L2 intersect at exactly one point, and find the coordinates of that point. Find a Cartesian equation for the plane that contains L1 and L2. Hint: use the cross-product on the two direction vectors to find a normal vector. а. b.

Q: 14. Which of the following planes is the equation for the plane with an x-intercept at P(2,0,0), a…

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Q: Suppose plane P contains the points A(5,0,-1), B (2,3, 2), and C(-2,1,–4), and assume P, is the…

A: The equation of the plane P1 containing A(5, 0, -1), B(2, 3, 2) and C(-2, 1, -4) is given by…

Q: (a) Find the point at which the given lines intersect. (2, 2, 0) + t(2, –2, 2) (4, 0, 2) + s(-2, 2,…

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Q: (vi) Find an equation of the plane that passes through the line of intersection of the planes x – z…

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Q: Line Li: 0.5C1- X)= 2 = 0.5z intersects the plane defined by B(2,237), C Cl,o, 12) at point P. Find…

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Q: The third question: Let Q be a point in space (1-,1-,1-) and let us have the line L whose equation…

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Q: The third question: Let Q be a point in space (1-,1-,1-) and let us have the line L whose equation…

A: For the solution follow the next steps.

Q: a) Find the area of ​​a rosette petal given by r = 3cos3θ b) Find the equation of the plane that…

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Q: Two planes x+ y – 27 = 3 and 2x – 3y + z = 1 intersect in a line. a Find the Cartesian equation of…

A: (a) Given that planes are x+y-2z=3 and 2x-3y+z=1 The cartesian equation of the two lines is,…

Q: b0 = -6, b1 = 5, b2 = 0a. determine whether the plane slopes upward, slopes downward, or is…

A: (a)Direction of the slope of a plane:If the sign of a partial slope is positive, the plane slopes…

Q: passing through the origin and point A (1,1,1) What is the equation for the plane perpendicular to…

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Q: Any plane passing through (-2, 2, 2) is A(x+2) + B(y – 2)+C(z- 2) = 0 : It passes through (2, –2,…

A: Solution of 3 variables linear equation is solved by using cross multiplication method.

Q: 2 x-4_y+2_ z-6 = 16 and a line 1 has equations -1 2 4 A plane II has equation r• 1 Show that the…

A: To find if the line lies on the plane

Q: x =1- 2t y = 2+3t I: The plane x+2y+2z=3 and the line are parallel z=2-21

A: Since, you have posted more than one question, we solve the first one for you. For the remaining…

Q: Intercepts Let a, b, c, and d be constants. Find the points at which the plane ax + by + cz = d…

A: Given plane ax+by+cz=d where a ,b, c and d are constants.

Q: Let Q(1,10,-1) be a point in space and a let us have the line L whose equation is 1 L: 1-x = 1- y :…

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Q: The line L: x = 3 + 2t, y= 2t, z = t Intersects the plane x + 3y – z = -4 in a point P. Find the…

A: The given line is: L: x=3+2t, y=2t, z=t The given plane is: x+3y-z=-4

Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

A: Given: 2x+5y=-7; x-38=y2=z-714 Let, x-38=y2=z-714=t ⇒x=8t+3; y=2t; z=14t+7

Q: Given a point P(1,1,2) and a plane a in R' defined by the equation 2a + y-22 = 0. (a) Find an…

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Q: T = -2+3s Consider the lines defined by the equations l1 : x – 2 = y – 1 = z + 4 and l2 : {y = -1+8…

A: To find the point of intersection of two lines we equate the values of x and y in two lines to find…

Q: (a) Find the point at which the given lines intersect. r = (3, 2, 0) + t(2, –2, 2) r = (5, 0, 2) +…

A: Consider the equations of lines

Q: Given plane z: 3x+2y+z-3=0, point P(1, -2, 3), and lines 1₁:1 and 4₂: (3, 6,-5)+1(2, 3, 1), find: a)…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve first three…

Q: (a) Find the equations of the line through the points (4, −1, 2) and (3, 1, 4).(b) Find the equation…

A: Since you have posted multiple subparts, as per our policy we will answer first three subparts.…

Q: 2: -1+t, y: 3+24, 019:0) show thet the lines う: 4-2t2 CAre parallel. b) Find th plane the determines…

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Q: Relay Question: (i) Find the distance from the point P(-1,2,1) to the plane II1 : 2x + y – 3z = 4.…

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Q: y = -1+3t and y 5-3s 4 t 2+4s (b) Find the plane that contains these two lines.

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Q: -1. Find an equation for the plane consisting of all points that are equidistant from the points (1,…

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Q: Question Find the equation of the Plane through the point (-1,4,2) that contains the line of…

A: Given: The equation of line of intersection of the planes are, 4x-y+z-2=02x+y-2z-3=0 The objective…

Q: Consider the lines below. r = ‹2, 2, 0› + t ‹2, -2, 3› r = ‹4, 0, 3› + s‹-2, 2, 0› (a) Find the…

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Q: Q/ Find the angle between the planes (x+y+2=1)and (x-24+32%-1).And find the Symmetric equations for…

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Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

A: Given line, x-14=y2=z-36And given plane3x+4y=-7Any  point on the line isx-14=y2=z-36=tx-1=4t,y=2t,…

Q: I = 10+ 2s I - 1 y +3 12 - z Consider the lines defined by the equations ( : and l2: 9. y = 5s z =…

A: We have to find intersection Point of given line and equation of plane which contain both line.

Q: (a) Find the point at which the given lines intersect. r = (1, 3, 0) + t(3, -3, 2) r = (4, 0, 2) +…

A: Introduction: When a line in three dimensional Euclidean geometry passes through a point with a…

Q: whose equation is L A point in space and let's Q(0,1, -1) let it be |have the line L: 3- 2x = 1- y…

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Q: Q2. Sketch the three points on 3-D coordinates. Then Find equation of the plane has P1 (3, 2, 1), P2…

A: A cartesian coordinate system contains 3 mutually perpendicular number lines named x axis, y axis…

Q: (a) Find the point at which the given lines intersect. r = (1, 2, 0) + (2, -2, 2) r = (3, 0, 2) +…

A: The vector form of the equation of a line is r=ro→+tv→. The equation of the plane containing the…

Q: The line L: x = 3 + 2t, y = 2t, z = t Intersects the plane x + 3y – z = -4 in a point P. Find the…

A: Given: The line L: x = 3 + 2t, y = 2t, z = t intersects the plane x + 3y - z = -4 in a point P.   To…

Q: Q2. Sketch the three points on 3-D coordinates. Then Find equation of the plane has P1 (3, 2, 1), P2…

A: Given points P1 =(3,2,1)P2=(2,1,-1)P3=-1,3,2

Q: Q3: Let L be the line of intersection of the planes 3x + y -z = 4 and 5x + y + 2z = 1 Find the plane…

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Q: 3) The line L: x = 3 + 2t, y = 2t, z = t_intersects the plane x + 3y -z = −4 in a point P. Find the…

A: The equation of the line L is given as x=3+2t, y=2t and z=t. The line intersects the plane x+3y-z=-4…

Q: (x = -2+ 3s and l2: y = -1+s z = 2 - 4s z+4 Consider the lines defined by the equations l1:x – 2 = y…

A: At the point of intersection of two lines, the coordinates becomes same thus use to to determine the…

Q: 2. Given point P = (1,2,1) and Q(3,3,0) Find b) the coordinates of the point M, where line L meets…

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Q: The equation of line given by the intersection of two planes with equations x + 2y-3z 4 and 2x – y+…

A: Option A is correct.

Q: (b) Find the point of intersection of the line 1,:r=-2i – 7k+ 1(i+ j-k) and the plane t: n+7y +…

A: Solution:

Q: Let A(1,1,1) B(2,3,4) and C(1.2,3) a) Find the equation of the plane containing the points A, B and…

A: Note: As per guidelines norm we can answer only one question with maximum three subparts. a) Finding…

Q: an equation of the plane that passes through the given point and is perpendicular to the Point…

A: Please refer to the image below

Q: Pr. #1) Find an equation of the plane. Contains the line = = z+ 2 and is orthogonal to the line r =…

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Q: Pr. #2) Find an equation of the plane. Contains the line r+3 = = and is orthogonal to the line r…

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Q: Po (2,1,-1) and perpendicular to the line of Find a plane that passes through intersection of the…

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