Write the equation of the plane with normal vector n = 4k passing through the point (7, 2, 5) in the scalar form ax + by + cz = d.

Q: Find a normal vector of the plane that contains the points (1, -2,0). (3, 1, 4) and (0, -1, 2).…

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Q: Find an equation of the plane. The plane through the point (1, 7, 2) and with normal vector 4i + j –…

A: Given:   Point : ( 1 , 7 , 2)  Normal vector : 4i + j - k

Q: Find a nonzero vector parallel to the line of intersection of the two planes 2y 5x - 3x = -5 and 5y…

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Q: write the equation of the plane with normal vector n passing through the given point in the scalar…

A: We have, Equation of plane through P0 =(x0, y0, z0) with normal vector n = <a, b, c> Vector…

Q: What are the components of vector p which has three times the magnitude of the normal vector of the…

A: Given plane: Let the normal vector be n. So,

Q: Find an equation of the plane that passes through the point P(-8, –3, 7) and has the vector n = (-8,…

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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: Parametrize the line that passes through the point (1,2,3) parallel to the vector v = -3i + 7k.

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Q: Find an equation of the plane through the point (2,1,-3) with normal vector 2i-3j+k. Determine the…

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Q: Find an equation of the plane. the plane through the point (5, 6, 5) and with normal vector 6i + 8j…

A: As we know that the equation of the plane which is passing through a point Px0,y0,z0  and normal…

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

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Q: Find a unit vector in the xy-plane that is orthogonal to

A: Here given vector as a=123 Consider a vector as b=25-150 Now find the dot product of vector b to…

Q: Write the scalar equation of the plane with normal vector - [0, – 1, O] and having a y-intercept 3.…

A: Equation of plane

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: snip1

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

Q: Parametrize the line that passes through the point (1, 2, 3) parallel to the vector v =-3i + 7k.

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

Q: Give an equation of the plane with a normal vector n = ⟨1, 1, 1⟩ that passes through the point (1,…

A: we know that equation of plane with a normal vector x0,y0,z0 and passes through point x1,y1,z1 is…

Q: Find the vector equation for the line of intersection of the planes 3x−2y+2z=1 and 3x+4z=−4 r=⟨ ,…

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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: Compute the normal vector to the surface Ф(и,0) %— (и? — 0?, и +0, и — 0) at that point (4,3).

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Q: What is the length of the vector whose initial point is (0, 1, -2) and (2, - 2, 3) 35 A. 38 В. V35…

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Q: Write the scalar equation of the plane with normal vector = [1, 2, 1)] and passing through the point…

A: here normal vector is  and the given point is

Q: A normal vector for the plane 4x −2y + 7z−11 = 0 is ______.

A: We have given equation of plane  4x-2y+7z-11=0 Then, we  can write this as…

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

A: Given; n=<7,-5,4> Point (1,-5,1).

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

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Q: Find an equation of the plane through the point (29,-37,46) and with normal vector 14i+19j–17k.

A: we have to find an equation of the plane passing through the point (29,-37,46) and with normal…

Q: Find a vector perpendicular to the 2-space line: Qx - Ny + R = 0

A: Please see the below picture for detailed solution.

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 a vector parametrization of the line through P = (0, –8, 7) in the direction v = (7, 0, 0)

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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: 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 in xyz-space through the point P = (4, 2, 4) and perpendicular to the…

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Q: Find the equation of the plane in xyz space through the point P= (3,3,4)and perpendicular to the…

A: We need to find equation of plane.

Q: Give a scalar equation for a plane at distance 9 from the plane P with equation -2x+y-2z = 3.

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Q: Express the vector H %3D p?za, + зфzaф - рф*а, at B(3, -4, 1), in CCS.

A: The given vector is H→=ρ2z aρ+ 3Φz aΦ - ρΦ2 aZ.We have to express it in the cartesian co-ordinate…

Q: A normal vector for the plane 4x – 2y + 7z – 11 = 0 is

A: Solution is given below:

Q: Parametrize the line that passes through the point (1, 2, 3) rallel to the vector V = -3i +7k .

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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: Is it true or false that the vector u (3, 3, –3) is a normal vector to the plane -x – y + z + 3 = 0…

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Q: Write the vector A = 2z1-xi + yk in cylindrical coordinates.

A: *concept:- cylindrical co-ordinate = (x, y, z).

Q: 3) Explain why the Cartesian equation 2x– 5y+ 3z = 2 does not describe the plane with normal vector…

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Q: Write an equation of the plane with normal vector n= (2,8, -4) passing through the point (3,-9,-5)…

A: Vector equation of plane is used.

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

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Q: Find the equation of the plane in xyz-space through the point P=(3,3,2) and perpendicular to the…

A: topic - equation of a plane

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: 2. Find the equation of plane which passes through the point (1,2, –3) and the vector i – 2j + 3k is…

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Q: Find an equation of the plane that passes through (4,-1,2) and has a normal vector perpendicular to…

A: Given An equation of the plane that passes through (4,-1,2) and has a normal vector perpendicular to…