Write vector and parametric equations of the plane a) parallel to the lines [x, y, z]= [1, - 2, 7]+ s[4, –1, - 3] and [x, y, z] = [7, - 2, 15]+ t[1, 6, -8] and through the point Po(-5, 9, -3) 2. b) through the points A(6, 1, 4), B(-3, 7, 9) and C(5, 0, 3)

Q: Find the vector and parametric equations for the line through the point P(2, 2, -2) and orthogonal…

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Q: Let A : x + 2y – z, B be the plane passing through the points (2, 1, 2), (1, 1, 3), (2, -1, 1), and…

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Q: 90. a. Determine the vector and parametric equations of the plane that passes through the points…

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Q: 6. Find the vector, parametric and scalar equations of the plane that contains the points A(-1,2,5)…

A: The points are A(-1, 2, 5) B(3, 2, 4) and C(-2, -3, 6) AB→=324--125=20-1AC→=-2-36--125=-3-51 The…

Q: Let ū = (0, 1, –1), v = (2, 1,0) and w = (4, 1, 1). a) Show that ū, ū and w lie in the same plane…

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Q: Determine the scalar, vector and parametric equations of the plane that passes through the points…

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Q: Find parametric equations for the line described below. The line through the point P(1, 1, -2)…

A: we have to find

Q: 8. Find a vector parallel to the line of intersection of the two planes a – 2y + z = 1, 2x + y + z =…

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Q: Find the vector and parametric equations for the line through the point P(-5, -3, -4) and the point…

A: Given: P(-5,-3,-4) and Q(-2,2,-5) To find the vector r(t) and the parametric equations for x(t),…

Q: 3. Find vector and parametric equations of the plane that contains the point P = (-3,1, 0) and is…

A: We have to find

Q: 1. Determine vector and parametric equations of the plane that contains the points A(1, 2, -1), B(2,…

A: Since you have posted multiple questions. we will solve first question only due to the bartleby…

Q: Consider the plane that goes through the point (4, 1, 3) and is orthogonal to vector (2, 3, 1). Find…

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Q: (5.1) Find the vector form of the equation of the plane that passes through the point P0 = (1, −2,…

A: Note : As per our company guidelines we are supposed to answer only one question. Kindly post the…

Q: Let A(1, 2, 1), B(3, 1, 2) and C(2, 1, 2) be points in R³. a) Find the point-normal form of the…

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Q: (a) Find a vector parallel to the line of intersection of the planes 4x + 3y – 2z = -5 and -5x + y –…

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Q: Find the standard form equation (using variables T, y, 2) of the plane P through the points…

A: When a plane passes through 3 points, then equation of the plane is given by-…

Q: (a) Find a vector parallel to the line of intersection of the planes -x + 3y + 4z : 0 and -x - 3y –…

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Q: 8) The point A(1,2,2) is a point on the plane with normal vector n= (-1,2,6) Determine the Cartesian…

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Q: Find the vector and parametric equations for the line through the point P(-5, 3, -1) and the point…

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Q: 2. Find the equation of the planes: a) (in general form) that goes through the three points A(4, 0,…

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Q: Determine the vector and cartesian equation of the plane that passes through the points A(−3, −2,0),…

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Q: 19. Find the Cartesian equation of the plane a) passes through point A(6,- 7, 4) and parallel to the…

A: To find the Cartesian equation of the plane, a)Which passes through the point A6,-7,4 and parallel…

Q: 1. Determine the vector and parametric equations of the plane containing the point (1, -5, 9) and…

A: Equation of plane

Q: 1. Find an equation of the plane containing the point P(3,2,7) and having a nor- mal vector i = (2,…

A: Given: Point on the plane:  A=(3, 2, 7)Normal vector to the plane is:  n→=2, 5, 2

Q: 5. (a) Consider the vectors u = (1,0, 1) and ē of the 2-dimensional parallelogram determined by…

A: we are given that

Q: 1- Determine the Eq. of plane (М) pass A(0,2,0) , B(1,1,1), C(-1,0,2) through points 2- Determine…

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Q: Find the vector and parametric equations for the line through the point P(-2, 1, -5) and the point…

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Q: Write the equation of the plane with normal vector n passing through point Po in the scalar form ax…

A: Topic = Vector

Q: The equation of a plane is (X,Y,Z)= (1,0,0) + s(-1,0,-1) + t(-1,2,0),s,t ER. Determine the vector…

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Q: 7. Find the vector and parametric equations of the plane that is parallel to the yz-plane and…

A: W e have to find the equation of plane.

Q: Please help solve #12. Thank you

A: To find the intersection line of the given plane with equations, axx + ayy + azz = C1  &  bxx +…

Q: 2. (a) Find an equation of the plane passing through the points (0,0, 1), (2,2, 1), and (1, 2,0).…

A: Equation of plane.

Q: Find parametric equations for the line through p (2,3,0) and perpen-dicular to the vectors u =(1,…

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Q: Which of the following are equations for the plane through the points P(1, 1, -1), Q(3, 0, 2), and…

A: First find PQ and PR , two lines on the plane

Q: b) Find parametric equations of the plane (P) containing the point P(1,-2, 0) and the vectors û and…

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Q: Find parametric equations for the lines in Exercises 1–4. 1. The line through the origin parallel to…

A: Hey, since there are multiple questions posted, we will answer the first two questions. If you want…

Q: (a) Determine the scalar, vector and parametric equations of the plane that passes through the…

A: Comment: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Let ü = (0, 1,-1), e - (2, 2,0) and i - (4, 2, 2). a) Show that ü, and w lie in the same plane when…

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Q: through the points O(0, 0, 0), A(1, −2, 3), and B(2, 0, −2); (ii) through the point A(1, −2, 3) and…

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Q: A) find a vector parallel to the line of intersection of the planes -3x - 2y - 2z = -1 and -4x - 2y…

A: Equation of line of intersection

Q: Find vector and parametric equations of the plane that contains the point P = (-3,1,0) and is…

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Q: Let P(1,1,-1), Q(1,2,0), and R(-1,0,0) be given points. Give the equation of the plane containing…

A: Given problem:- Let P(1,1,-1), Q(1,2,0), and R(-1,0,0) be given points. Give the equation of the…

Q: b) A VECTOR form equation of a plane that contains the following lines: L: (x,y,z) (1,0,- 3) +…

A: The equation of the lines are given L1: (x,y,z)=(1,0,-3)+t(2,4,-1) and L2:…

Q: 22. Determine the vector and parametric equations for the line passing through the points P(-1,-3)…

A: “Since you have posted multiple questions, we will solve the first question for you. To get the…

Q: Pls help on these questions and pls explain thoroughly.

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Q: a) Find the plane equation which contains the line L given by x = 1-t,y = 1+2t, z = 2– 3t and the…

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Q: 14. Given the vector form of a line in three-space to be [x, y, z] = [2,6, – 3] + t[4,10,6], find a.…

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