28. Given that points A(1,3,1), B(4,–1,2), C(12,0,1) and D(0,2,0) Find a. a vector equation of the line AB. b. an equation of the plane ABC in the Cartesian form c. the acute angle between the plane ABC and the plane ABD

Q: Find the equation of a plane that is perpendicular to the vector 4 i + 2 j - 2 k and passing through…

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Q: Is the line x = 9- 8t, y= 4 + 2t, z= - 5t parallel to the plane 2x + y-z=2? Give reasons for your…

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Q: Find the equation of a plane that is perpendicular to the vector – i+ 2j+ 2k and passing through the…

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Q: Show that the lines determined byr 1(t) = <−2 − 5t, 3 + 2t, 4t >andr 2(t) = <8 + 15t, 1 −…

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Q: A linear combination of of u = 3 and v= 4 will give a plane in R³. Given that the point (2, 1, −1)…

A: Consider the given linear combination, u=132 and v=-144 will give a plane in ℝ3. The equation of a…

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: Given the points A(2,6,0) and B(3,5,6) determine the equation of a line vector in parametrix form

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Q: Let U = (2,1,0), V = (1,0,1), and W = (2, −1,1). Find the plane through U, V, and W, expressed in…

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Q: Give the symmetric equations of the line l perpendicular to the plane T : 5x – 2y = z+4 and passing…

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Q: 4. Find an equation (in point-normal form) of the plane containing the points K, M, and N. 5. Let R…

A: This is a problem of Vector Algebra.

Q: 4. (a) Show that the line l given by l: 1= 2+3t, y=1+4t, z= 5+ 2t, te R, lies in the plane II given…

A: Given problem:- Show that the line  given by   l : x = 2 + 3t , y = 1 + 4t , z=5+2t ,t in R   lies…

Q: The equation of the plane passing through the point A(6, 6, 6) and orthogonal to the line a = 11 +…

A: The objective is to find the equation of the plane passing through the point A6,6,6 and orthogonal…

Q: Find the equation of a plane that is perpendicular to the vector 3 i - 4j+ 5k and passing through…

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Q: Consider the planes x – 10y – 2z = 3 and 2x – y + z = -13. Find the following. 1. A vector…

A: The given planes are: x-10y-2z=3 and 2x-y+z=-13 Let us assume z=t on the line of intersection, where…

Q: Suppose a line is given parametrically by the equation L(t) = (-4t, –4 – 3t, 4 + 4t) Then the vector…

A: topic - equation of line

Q: If the plane ar + by + cz = 30 through the points P(4, 1, 2) and Q(2, 3, – 1) is orthogonal to the…

A: Given plane passing through the given point P and Q

Q: Show that the lines L1 : x =1– t, y = 2t, z = 4+t and L2 : x = 1+ 3t, y= 3 – 6t, z = 5 – 3t are…

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Q: Suppose that the line e is represented by r(t) = (10+ 2t, 14 + 6t, 23 + 8t) and the plane P is…

A: Please refer the attached image for complete solution. THANK YOU.

Q: a) Explain fully, atleast three possible relationships between two lines in R3 [c3] b) Which of the…

A: (a) The relationship between any two lines in ℝ3 is always one of the following three: They can be…

Q: Find parametric equations for the line through P(8, −7, 9) perpendicular to the vectors A = ⟨3, −1,…

A: NOTE: Refresh your page if you can't see any equations. . the given point is  given vectors are

Q: Which of the following is a direction vector for the plane with Cartesian equation 3x -2y - 5z + 3 =…

A: To find a direction vector for the given plane. The general form of plane with cartesian equation…

Q: 19. Given that A is the point (5,-1,2), I is the plane with vector equation: r. (2i + 6j + 9k) =…

A: Plane and line.

Q: Suppose a line is given parametrically by the equation L(t) = (4+ 3t, -4 – 5t, 2 – 2t) %3D Then the…

A: Compare with general equation of line in parametric form

Q: If A(1,2.-1) B(3.6-7), c(2,3.-3) D(3.4,-3) Calculate the angle between the vector Projection of ÄB…

A: According to question given that A(1,2,-1)B(3,6,-7)C(2,3,-3)D(3,4,-3)Angle between a pair of lines…

Q: Suppose (-2,0, 6) is a point on the plane o, and the the line r(t) = is contained on the plane ɔ.…

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Q: find the equation of the plane with the given description. Passes through O and is parallel to 4x −…

A: Solution:Given    A plane 4x − 9y + z = 3To find the equation of the plane passess through O and is…

Q: c) Is the point (4,3, 3) on the line (L1) ? Why or why not ? d) Determine the vector equation of the…

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

A: Given, Line-> r(t) = (2, 1, 3) + t(3, -3, 1) Plane-> 4x - 4y - 2z = 6 ------equation 1

Q: W,X ,Y,and  Z have the position vectors 3i+3j-4k, 4i+j+k, 2i+3k and 3i+j-4k respectively.…

A: The given position vectors areW = 3 i^ + 3 j^ - 4 k^X = 4 i^ + j^ + k^Y = 2 i^ + 3 k^ Z = 3 i^ +  j^…

Q: Given the points P = (2,3,4), Q = (4,–1,5) and R = (-2,5,6) : a. Find a parametric or vector…

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Q: 27. Are the points P(1, 2), e(7,3), and R(-2, 1) on the line with vector equation = (19,5) + s(6,1),…

A: According to our terms and conditions I have solved first question for next question repost

Q: 3. Consider the plane TT: 4x + 3y - 2z + 12 = 0. What is the relationship of the plane to each of…

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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: Q1-)A-) Find the distance from the point (0,1,1) to the line of intersection of the planes : x + 2y…

A: Given: A) Point (0, 1, 1) and the planes x + 2y + z = 1, x - y + 2z = -8. B) Vertices of triangle…

Q: Determine the Point OF 3x +y+22 = 45 and the Line witth plaremetre eg dartons 1 = 1+t, y= 3 +2 € ,…

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Q: 6. If the plane ax + by + cz = 30 through the points P(4, 1, 2) and Q(2,3, -1) is orthogonal to the…

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Q: Find the equation of the plane that contains the line r¡(t) = (1 + lt, –1+t, 2+ 8t) and the point…

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Q: Consider the points K (−1, 0, 7) and M(1, −2, 5), the vector MN = (1, 4, −3), and the line  I with…

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Q: Find the equation of the plane through P(2, – 1,1) that is parallel to Il: 2x + 3y + z – 12 = 0. %3D

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Q: Suppose that the line l is represented by r(t) = (13 + 2t, 26 + 6t, 12 + 2t) and the plane P is…

A: Given line l : r(t)=13+2t, 26+6t, 12+2t and the plane is P : 2x-2y+5z=25 1. Let the point of…

Q: Q1:A-Find the equation of plane passes through (0,2,-1) parallel to the plane 3x+y+z=7? b- Find…

A: 1. A. According to question,Given plane,3x+y+z=7,Given Point 0, 2, -1

Q: is a vectors problem - Simple solutions would be better, not too advanced Question: For what…

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Q: Given the planes 3x – 6y – 2z = 15 and 2x + y – 2z = 5 anser the following. (a) Find a vector…

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Q: Consider the points K(−1, 0, 7) and M(1, −2, 5), the vector MN = , and the line L with symmetric…

A: We have to solve given problems:

Q: = 30 through the points If the plane ax + by + cz P(4, 1, 2) and Q(2,3, –1) is orthogonal to the…

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Q: c) Find an equation of the plane that contains the line L: 1=1-t, y = 2+t, z = -3t where teR and the…

A: Equation of plane that contains the line x=1-t, y=2+t, z=-3t where t is in R and the point…

Q: Let M be a plane that contains the point with coordinates (-2,-2,-1) and is orthogonal to the vector…

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Q: 5) Consider the vector ū = (1,2, –2) and the points Q(6, 5, 2) and R(3,0, 0). Answer the following…

A: Plane and vector

Q: For what positive value of c is the acute angle between the plane containing the points A(0,0,1),…

A: Calculate the vector normal to the yz plane. Equation of yz plane:x=0Equation of vector normal to yz…

Q: . Find the acute angle between the line joining A(1,2,3) and and the plane containing point…

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.