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 positioned so that their initial points coincide, b) Find parametric equations of the plane (P) containing the point P(1,-2,0) and the vectors ü and e. c) Find Proj, ü.

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

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Q: Find both the vector equation and the parametric equations of the line through (0,0,4) in the…

A: Explanation of the answer is as follows

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

A: Vectors u ,v and w lie in same plane if u.(vxw) = 0 Here u = (0,1,-1) v = (1,1,0) w= (2,1,1) 3…

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: Find the scalar equation of the plane that contains (1,1,1), (3,-1,5), and (4,2,-2). -2x1 + 9x2 + x3…

A: Equation of the plane, passing through three points

Q: Let U = (2,1,0), V = (1,0,1), and W = (2, −1,1). Find the intersection of this plane with the line…

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Q: ) Find a vector parallel to the line of intersection of the planes −4x − 2y + z = −7 and  5x +2y −…

A: (a) Given planes are −4x−2y+z=−7 and 5x+2y−5z=12 We have to find the vector v→ parallel to the line…

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: 4 - x y + 1 %3D 2 1 3 L2 :[x, y, z] = [-2,4,3]+ t[-6, 5, 7], t E F

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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: Let u = -i + j, v = 3i - 2j, and w = -5j.Find specified scalar 5u . (3v - 4w)or vector.

A: It is given that  u = -i + j, v = 3i - 2j, and w = -5j

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

A: Answer

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: 13. Find an equation of the plane through the point (1,2,3) and perpendicular to the vector…

A: Given a point P( x, y, z) and a vector (a, b, c) which is perpendicular to the given plane

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: 1. Let II, be the plane passing through the point (7, 1,6), and that contains the line r(t) = (1,0,…

A: Given that π1 be the plane passing through the point (7,1,6), and that contains the line…

Q: Let u = -i + j, v = 3i - 2j, and w = -5j.Find specified scalar 4u . (5v - 3w)or vector.

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Q: Determine vector and parametric equations for the line in R that passes through the points A(1,0, 1,…

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Q: The equation of a plane n ·〈x, y,z〉= d is said to be in normal form if n is a unit vector. Show that…

A: Given :           The equation of a plane n . <x, y, z> = d is said to be in normal form if n…

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: Find a vector parallel to the line of intersection of the planes 5x−y+2z=4 and 4x−y−3z=0v→=  (b)…

A: Find a vector parallel to the line of intersection of the planes 5x−y+2z=4 and 4x−y−3z=0

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: The Cartesian equation of the straight line tangent to the plane curve given parametrically by the…

A: This question can be solved using the concept of tangent and normal under application of…

Q: Let the solid form in the orthogonal coordinate system xyz be surrounded by points A, B, C, D and F,…

A: The given co-ordinates of vertices are A = (-4, 1, 3), B = (6, 1, 1), C = ( 9, 5, 0), D = (4, 5, 1),…

Q: Represent the line segment from P to Q by a vector-valued function and by a set of parametric…

A: Two vectors Px1,y1,z1 and Qx2,y2,z2 Line segment P to Q: 1) Parametric form is…

Q: 10.Determine the vector equation of the plane that contains the origin and the intersection of:…

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Q: Determine the vector, parametric, and Cartesian (Scalar) equations for the line that passes through…

A: To find the equation of line that passes through the point A(4,-1) and is also perpendicular to line…

Q: A line l passes through the point P(2,4, 3) and is parallel to the vector (3, 2, –3). | At what…

A: Proceed as shown below

Q: Determine the scalar equation of the plane containing the point (-2, 9, 7) and 9. perpendicular to…

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Q: Let v =5j and let u be a vector with length 3 that starts at the origin and rotates in the xy-plane.…

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Q: (a) Show that the point P(5,0,0) lies in the plane r + 2y + 6z = 5 and the point Q(1, –2, 4) does…

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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: Calculate the coordinates of the vector w obtained by rotating anticlockwise the vector v= [0, -1,…

A: When a coordinate is being rotated along the direction of a vector by a certain angle, the new…

Q: Find parametric equations for the line through the point P(-5,6,7) and perpendicular to the vectors…

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Q: Suppose the light source is placed directly above the xy-plane, so the light rays come in parallel…

A: Given that,  If suppose the light source is placed directly above the x y - plane, so the light rays…

Q: Find the vector and parametric equations for the line through the point P(-4, -1, -3) and orthogonal…

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Q: (a) Find a vector parallel to the line of intersection of the planes 4x – y – 3z = 6 and -5x + 4y –…

A: According to question given thatplanes equation 4x-y-3z=6-5x+4y-4z=3

Q: Let ri = xi+y1j+2ık, r2 = x2i+ Y2j + zzk and r3 = x3i+ Y3j+ z3k %3D be the position vectors of P…

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Q: Find a vector that is orthogonal to the plane containing the points P = (3,0, 1), Q = (4, –2, 1) and…

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Q: Write the parametric and scalar equations of the plane given its vector equation [x, y, z] = [4, 3,…

A: Parametric equation is simple: x = 4 + 2s + 6t y = 3 + s + 6t z = -5 + 4s - 3t

Q: Find a parametric representation for the plane that passes through the point (2, –3, 4) and contains…

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

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Q: Let u = -i + j, v = 3i - 2j, and w = -5j. Find the specified scalar or vector: proju (v - w)

A: Given that, u = -i + j v = 3i - 2j w = -5j Then we get, v - w = (3i - 2j) - (-5j) = 3i - 2j + 5j =…

Q: (a) Find a vector parallel to the line of intersection of the -2. 3y - 4z planes -x + 3y + 4z = 0…

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Q: The vector u = i - 2j + 2k is positioned at a point P in space with coordinates: (x, y, 2) = (1, 2,…

A: Given:    The vector u = i-2j+2k is position at a point P in space with coordinates: (x, y, z) = (1,…

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.