(2) Determine if the following statement is true. Give an explanation. The plane z+y+ z =1 and the line z=t, y=t, z=tare perpendicular. (3) Find an equation of the plane that contains the line z =1-t, y=1+t, z = 2 and the point (1, 1,1). (4) Specify the domain of S(z,9) = . You don't have to sketch it. (6) La f(z,9) =="y? +zy (a) Find fa (b) Find fur (6) Skench the level curves of f(z, y) - V+ for a1,2,3.

Q: 1. Find the equation of the plane that contains the point (-1, 1, 2) and the line given by x=1-t,…

A: This question is based on 3d geometry.

Q: Find an equation for the plane that contains the line v = (-1, 1, 2) + t(9, 5, 4) and is…

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Q: 1 Find equation of plane which is containing Points A(2,1,1) and B(7,5,2) and normal to 2 x - 3y -…

A: We have to find the required plane

Q: 1. The plane containing the point (1,-5,8) and orthogonal to the line given b x=-3+15t, y=14-t,…

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Q: 1. Find an equation of the plane that contains the line r = -2+ 3t, y = 4+2t, z = 3 - t and is…

A: We have to find

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

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Q: An equation of a plane P passes through the point (0,0,-3) and perpendicular to the line L:x = 1-2t,…

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Q: Example 8: Find the point where the line 2t, and z = -3t intersects the plane x = 1 + t, y = –…

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Q: (A) Determine the plane that contain the point A(2,5,1) and the line L, t=x-2, 3t =y-1, t=z+1

A: The equation of the line L given in the parametric form, that is, Thus, the above equation of the…

Q: 3. Find the general form of the equation of the plane containing the point Q(0, -2, 10) and the line…

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Q: The intersection point of the line that passes through the origin and is perpendicular to the plane…

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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,…

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Q: 2.) ( the plane 2x-3y+z =6, and is parallel to the line of intersection of the planes x-2y+z=4 and…

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Q: 3. Find the plane determined by the intersecting lines L: x = -1+t, y = 2+t, z = 1- t; L2: x = 1 -…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: Consider the plane P with equation -2x+2y-z =3 and line L with equations x= -3-3t y = 3+7t z= 21…

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Q: Consider the plane P with equation 2x+y-2z = 4 and line L with equations x =-5+2t Ly =-5+6t z = 4-4t…

A: Given equation of plane P is 2x+y−2z=4 and equations of line are x=−5+2t, y=−5+6t, z=4−4t. And given…

Q: 10) Find the point of intersection of the lines L4:x = 1+ 2t, y = 2 + 3t, z = 3 + 4t and L2: x = 2 +…

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Q: 3. Let II: x - 4y + 2z - 7 = 0 be a plane in space and let & be the line given by the intersection…

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Q: 1. Consider the plane II1 : 3z + 2y + x = 2. (a) If II2 : 2z – 3y = 1 is another plane. Are the…

A: Here we solve the three dimensional geometry problem.

Q: 2. Find an equation of the plane that contains the line r = 1 +t, y = 2 - t, z = 4 – 3t, and is…

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Q: Consider the plane P with equation 2x-2y+z =4 and line L with equations x= 3+2t y =-1-5t z= 5+4t…

A: Solved below

Q: Let L be a line which passes through the point (-6,0, 1) and is perpendicular to the plane r + 2y +…

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Q: Find an equation of the plane. The plane that passes through the point (1, 2, 4) and contains the…

A: Topic = Vector correct answer e

Q: Find the point of the intersection of the plane P: 2x- 3y + 4z + 14 = | 0 and the line L:x =1-t, y =…

A: See the attachment

Q: Find an equation of the plane. the plane that contains the line x = 2 + t, y = 3 - t, z = 5 - 3t and…

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Q: Q1) the plane has equation of 4x-3y-2+5=0 Pud equation of plane partlel to R) and contimons with…

A: Given that: Equation of given plane is: 4x-3y-245=0and contains point (2,1,3)

Q: Find the equation of a plane that passes through the origin and contains the line x = 2t, y = 3t, z…

A: Consider the provided question, The equation of a plane passing through the point (x1, y1, z1) is…

Q: Suppose we need to find an equation of the plane that passes through the line of intersection of the…

A: Since, we know that equation of a plane passing through the intersection of planes P and Q is given…

Q: 9. Find the equation of the plane through P(1,1,4) that is parallel to the plane x+ 5y – z + 8 = 0

A: The scalar equation of parallel planes differ only by a constant Therefore, equation of the required…

Q: 5. Find the Cartesian equation of the plane that has a z-intercept of 3, a y-intercept of -2, and is…

A: Explained below

Q: Consider the plane P with equation x+2y+2z =-10 and line L with equations x =-1+2t y =-1+3t z = 1+5t…

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Q: Find the point where the point P(1,3,4) is symmetrical with respect to the plane D:3x-2y+z+6=0

A: In this question we will use basic of geometry i.e image of a point in a plane. Solution of the…

Q: Suppose the solution set of x1 + x2+2x4 What are the equations of the plane at (1,2,3,4) which is…

A: First we find direction vectors of the plane of solutions.

Q: Find an equation of the plane. The plane that passes through the point (3, 4, 5) and contains the…

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Q: 6) Consider the plane P : x+y – z = 0 in R³ that contains both the points P(1,0, 1) and P2(0, 1, 1).…

A: • In the first part, we have to use the general Cartesian equation of a line passing through two…

Q: Let L be a line which passes through the point (-4, 0, 1) and is perpendicular to the plane x + 2y +…

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Q: Let L be a line which passes through the point (-4, 0, 1) and is perpendicular to the plane z + 2y +…

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Q: 31. Determine the point of the plane T: 15x - 3y + 2z + 6 = 0 intersection of the line [x, y, z] =…

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Q: 2. Find an equation of the plane containing the point P (0, -) and the line determined by the two…

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Q: At which point does the line described in question 3 intersect the plane described above? (Hint: You…

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Q: 2) Find an equation of the plane that contains all points that are equidistant from the points…

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Q: Q3/ Find the plane determined by the interseetiny Lines L X=1-2t, , 3-st,,そニ-2+t, La.Xe-3+t2)…

A: To find equation of plane we need to first find point and direction ratio of lines. Then find…

Q: The intersection point of the line that passes through the origin and is perpendicular to the plane…

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Q: Let L be a line which passes through the point (-4, 0, 1) and is perpendicular to the plane x + 2y +…

A: The line L is perpendicular to the plane, x+2y+4z = 0 Hence the direction ratios of the line L is…

Q: Find an equation of a plane containing the line r=⟨0,−5,−1⟩+t⟨−2,4,−2⟩ which is parallel to the…

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Q: Consider the plane P with equation x+2y+2z=-7 and line L with equations x=-4-2t y=4+7t z=-1+3t…

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Q: 3) Find an equation of the plane which contains the points P(-1,2,1), Q(1, –2, 1) and R(1,1, –1).

A: Equation of a plane passing through 3 points P(x1,y1), Q(x2,y2) and R(x3,y3) is given by,…

Q: 3. Find the general form of the equation of the plane containing the point Q(0, -2, 10) and the line…

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Q: 4. Determine the general equation of the plane containing the points P(1, -4, –5), Q(2,0, 13) and R

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