Find the equation of the plane in xyz-space through the point P=(2,5,5) and perpendicular to the vector n=(1,−4,−5).

Q: Find the vector equation for the line of intersection of the planes 5x +y-3z= -3 and 5x + z = -1 r =…

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Q: Find an equation of the plane that passes through the point (1, 3, −7) and is perpendicular to the…

A: Direction ratio of the line n=j is (0,1,0)  Given that the line is perpendicular to the plane.  So…

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

A: We need to find a vector parallel to the line of intersection of the planes 2x+3y-z=11 and 4x + 2y -…

Q: Find the vector equation of the intersection of the plane x+2y+3z=2 and x+3z=3  r=<  ,  , 0…

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Q: Consider the vectors a = (-1,–2, 3), b = (3,0, –2), v = (2, –5, –4) and the plane P given by 2x + y…

A: The given vector is; a→=-1,-2,3b→=3,0,-2v→=⟨2,-5,-4⟩and Plane P is;2x+y=z+13⇒2x+y-z=13…

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 the distance from the origin to the plane through the point (-6,3, -2) and having 5i - 3j° + 4k…

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Q: Find the general equation of the plane spanned by

A: Given vectors are 111 and 321

Q: Find an equation of the plane passing through (0,-2,3) that is orthogonal to the planes 2x+ 2y-5z 0…

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Q: What is equation of the plane passing through the point A(-2,-1,-3) and paralleto the vectors a=3+2k…

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Q: Find an equation of the plane. The plane through the point (2, 3, 6) and with normal vector 8i + j…

A: We will solve the problem.

Q: Find an equation of the plane. The plane through the point (2, 9, 6) and with normal vector 7i + j –…

A: Find an equation of the plane

Q: Find an equation of the plane. The plane through the point (8, 7, 1) and with normal vector 7i + j -…

A: The equation of the plane is given as:

Q: Find the vector n= normal to the plane passing through the points (0, -3, 0), (2, -1, 0) and (-2,…

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Q: snip1

A: we have to find the normal and general forms of the equation of the plane that contains the point…

Q: Find a vector parallel to the line of intersection of the planes 2x + y - 3z =13 and x + 3y + 5z =-8

A: Given, The equation of the planes  2x+y-3z=13 x+3y+5z=-8 We have to find a vector parallel to the…

Q: Find the equation of the plane through the point (-3,2, 0) and perpendicular to the vector (1,-2,5).

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: The plane contains the point (2, −1, 6) and is normal to the vector <2, −1, 6>.

A: Given: A plane passes through the point 2, -1, 6 and normal to the vector 2i^-j^+6k^.

Q: Find a vector equation for the curve of intersection between the surfaces y^2-x^2=9 and 2x-3y-z=12.

A: Introduction: We can determine the vector equation of the curve formed by the intersection of two…

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: Find the two vectors of length 1 normal to the plane given by the equation 3x – 2y + 4z = 7. -

A: From the plane equation we will get the direction ratio of normal. As the length of the required…

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 the vector equation for the line of intersection of the planes 3x−2y+2z=1 and 3x+4z=−4

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Q: Find a unit vector perpendicular to plane PQR determined by the points P(-3, 3, -4), Q(4, -1, - 23),…

A: Given query is to find unit vector perpendicular to PQR.

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

A: The direction vector of the line of intersection of two planes is parallel to the cross product of…

Q: s the vector ở = (-1,–2,3) perpendicular to the plane 3x + 6y – 9z + 5 = 0? %3D

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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

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. The plane through the point (6, 1, 5) and with normal vector 5i + j -…

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Q: Find a vector parametrization of the line through P = (3, -5, 7) in the direction v = (3, 0, 1)

A: Given:P=3,-5,7v=3,0,1

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: The scalar equation of the plane with normal vector [4, -1, 9] and passing through the point (2, -1,…

A: The scalar equation of the plane with normal vector [4, -1, 9] and passing through the point (2, -1,…

Q: Show that the point 1, - 2, 0 lies on both planes 3x-2y+z=7 and x-4y-2z=9. Hence, find the vector…

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Q: Find an equation of the plane that passes through the point Po(0,2, – 2) with a normal vector n =…

A: Find an equation of the plane that passes through the point p0 (0,2,-2)with a normal vector…

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

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Q: 4. Determine a vector equation for the plane that is parallel to the xy -plane and passes through…

A: Due to our answering guidelines we can only answer one question at a time, therefore I will be…

Q: Find an equation of the plane that passes through the point (3, 2, 2) and is perpendicular to the…

A: equation of the plane passing through the points (3, 2, 2)               A(x-3)+B(y-2)+C(z-2) = 0…

Q: Write an equation of the plane with normal vector n (7,5, −4) passing through the point (1, −5, 1)…

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Q: Find the equation of the plane containing the points P = (−1, 3, 2),Q = (−5, 1, 1), and R = (6, 0,…

A: Given,             The plane containing the points P = (−1, 3, 2), Q = (−5, 1, 1) andR = (6, 0, −3).

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: The scalar equation of the plane with normal vector [4, -1, 9] and passing through the point (2, -1,…

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Q: Find an equation of the plane. The plane through the point (4, 8, 6) and with normal vector 7i + j -…

A: Given, The plane passing through the point (4,8,6) with the normal vector 7i+j-k We know that, The…

Q: Find a nonzero vector parallel to the line of intersection of the two planes 5y – 4x + z =-1 and –…

A: The line of intersection of two planes is orthogonal to their respective normals.

Q: Find the linear equation of the plane through the point (2, −2, 6) and with normal vector j+2k.

A: Explanation of the solution is given below...

Q: Write the scalar equation of the plane with normal vector * - [3, 4, – 1] and passing through the…

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Q: Write the equation of the plane with normal vector n = (1, 3, 4) passing through the point (3, -1,…

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Q: Find the vector equation for the line of intersection of the planes 4x + 2y + 2z -1 and 4x + z= -2…

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Q: perpendicular

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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.