Find the equation of the plane E passing through the point P(2,3,1) and parallel to the vectors K = (-1,2,1) and Z = (3,1,0). A) 4x – y – z + 7 = 0 B) -4x + y – z – 7 = 0 C) 2x + 3y + z + 10 = 0 D) 2x – 3y + z = 0 E) -x + 3y – 7z = 0

Q: Find two vectors that are orthogonal to the plane containing the points P = (4,-2,1) and R =…

A: We find two vectors that are orthogonal to the plane containing the points P = (3,0,1), Q =(4,-2,1)…

Q: If the plane ax+14y+cz=30 through the point P(2,3,−1) is orthogonal or perpendicular to the plane…

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Q: Find a vector parallel to the line of intersection of the planes 2x + 3y – = =11 and 4x + 2y – 3= =…

A: Topic:- vector

Q: 1) in triple dot of vectors |(A x B). C = |(CX A). B\, where the vectors A, B, and C are not same…

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Q: Find the scalar equation of the plane that contain the line 7 = [2,1,7] + t[0, 1, 0], t e R and is…

A: Here we will find out the required plane.

Q: . Find two vectors that are orthogonal to the plane containing the points P = (3,0,1), Q = (4, -2,1)…

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Q: Find a vector v parallel to the intersection of the planes - (2x + 4y + 3z) = 4 and 3x + y + z = 7.

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Q: u.v<0, u.w < 0 ,w .u < 0 ?

A: Given data:     The given first vector is: u. The given second vector is: v. The given third vector…

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

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Q: 3. Two lines in the plane are perpendicular when the product of their slopes is -1. Apply this to…

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Q: Find a vector function that represents the curve of intersection between the paraboloid 2 z = 4x² +…

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Q: Find a nonzero vector parallel to the line of intersection of the two planes 3x−3y−4z=5 and…

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Q: Find an equation for the plane passing through the points Q(-2, –1, 1), R(-4, 2, 1), S(-5, –1, 2).…

A: We have been given 3 points : Q(-2,-1,1) R(-4,2,1) and S(-5,-1,2). We have to find the equation of…

Q: Find an equation of the plane through (-3, 8, – 7) that is perpendicular to the planes 6x – y +z = 4…

A: We need to find equation of plane.

Q: Find the vector equation of the line of intersection of the planes x+y+z=1 and x+2y+2z=1.

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Q: The vector parallel to intersection line of the two planes 4x-y+z=2 and 2x+y-2z=3 is: O0 -3i+6j-3k…

A: Two planes are given: 4x-y+z=2 and 2x+y-2z=3

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

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Q: Determine the Cartesian Equation of a plane that has a normal vector (6,-5,12) and passes through…

A: NOTE: Refresh your page if you can't see any equations. . The normal vector is  and the given point…

Q: Which of the following is the equation of the plane passing through the point (0,2,-3) and with…

A: Use the direct formula for equation of plane passes through a point and with given normal vector.

Q: Find an scalar equation of the plane containing the line x = 2 – 4t, y = 4 – 5t and z = 5+t and the…

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Q: Find a nonzero vector orthogonal to the plane through the points P, Q and R if P(1,0,0), Q(7,8,0)…

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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…

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

Q: Find a vector v→parallel to the intersection of the planes 3x+y+2z=3 and       −(x+2y+4z)=7

A: Vector parallel to intersection of two planes is cross product of the normal vectors of the two…

Q: Find an equation of the plane through (-7, 2, –6) that is perpendicular to the planes 4x – y + z = 4…

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Q: Find an equation of the plane passing through (0,-1,3) that is orthogonal to the planes 3x+4y-2z=0…

A: Let's find equation of the plane.

Q: Write the equation of the plane with normal vector n = 4k passing through the point (7, 2, 5) in the…

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Q: Find the vector equation for the line of intersection of the planes 2x – 2y – 5z = 5 and 2a + 2z = 1

A: Given  equation of planes 2x-2y-5z=5 2x+2z=1

Q: Give the general equation of the plane satisfying the given condition. plane Σ containing the point…

A: We will find the equation of the plane Σ which is parallel to the plain 2x − 6y + 3z = 0 and…

Q: find the vector equation of a plane that contains the intersection line of x + y + z = 1 and x – y +…

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Q: Find an equation of the plane through the origin that is parallel to the plane 4x – 3y + 5z + 10 =…

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Q: 4

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Q: Find a vector v parallel to the intersection of the planes 3x + y + 2z = 3 and – (x + 2y + 4z) = 7.

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Q: Find an equation for the plane passing through the points Q(2, 1, –1), R(-1, 3, –1), S(3, 1, 0). 1.…

A: We know that equation of a plane is given by ax+by+cz+d=0 As it passes through (2,1,-1), we get…

Q: The equation ax + by + cz = 0 represents a plane through the origin in R3. Show that the vector n2 =…

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Q: a. Find a unit vector perpendicular to the plane of P (4,2,1), Q (1,2,0), R (1,1,2). Whereas P is a…

A: Due to Bartleby guidelines, only 1question can be solved. Please repost the remaining questions to…

Q: Find an equation of the plane passing through (0,−3,1) that is orthogonal to the planes 5x+5y−4z=0…

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Q: Find an equation of the plane through the origin that is parallel to the plane 5x – 4y + 6z + 10 =…

A: Here we have to find the equation of a plane.

Q: Write the equation of the plane with normal vector n = 4k passing through the point (7, 2, 5) in the…

A: The equation of plane with normal vector (a,b,c) passing through the point p0 =(x0 ,y0 ,z0 ) is…

Q: 2. Can three vectors in the xy plane R2, have u v < 0, v w < 0, w u<0?

A: Given that, u, v and w are vectors in XY plane. The dot product of vectors is defined as, if u = a1…

Q: generate a parametrization of the line through P(2, -4, 7) parallel to v1 = 2i - j + 3k. Then…

A: We know that equation of line through (x1,y1,z1)  and parallel to ai+bj+ck is

Q: Find the vector equation of the line of intersection of the planes x+y+z = 1 and x+2y + 2z = 1.

A: The equation of the line vector of the intersection of 2 planes can be calculated using the cross…

Q: Find the value of d in the equation of the plane ax+by+cz+d=0 passing through the point P(3, 1, -2)…

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Q: Determine the scalar equation of the plane that passes through (5, -5, 5) and is perpendicular to…

A: Here we will find the required equation of the plane,

Q: Determine the Cartesian Equation of a plane that has a normal vector (6,-5,12) and passes through…

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Q: 32. a) Determine the vector equation of the line of intersection of these 2 planes: x + 2y + 2z = -3…

A: According to Bartleby guidelines I can only answer the first question of the given two problems.

Q: Find an equation of the plane through the origin that is parallel to the plane 4x – 3y + 6z + 18 =…

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Q: Determine the Cartesian Equation of a plane that has a normal vector (6,-5,12) and passes through…

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Q: Consider the plane that goes through the point (4, 1, 3) I to vector (2, 3, 1).

A: It is given that the plane is passing through the point (4,1,3) and orthogonal to the vector (2,3,1)…

Q: 5) Determine whether the plane 3x – 4y + 5z = 0 and the plane – 6x + 8y – 10z 4 = 0 are in…

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.