n equation of the plane with normal vector n= (-3, –3, –9) passing through the point (-4, 7, –9) in scalar fort = 360

Q: Find the normal vector to the plane that contains the point (1, 1, 3) and the line r(t)=(0,1,…

A: Let P be the point 1,1,3.Q be the point 0,1,2 on the line.Then, PQ→ = 0-1,1-1,2-3=-1,0,-1And the…

Q: Find a unit normal vector to the plane passing through the points P(1, 0, 0), Q(3, 2, 0) , and R(0,…

A: Since you have asked multiple questions in a single request, we will be answering only the first…

Q: Find the linear equation of the plane through the point (6,−2,5) and with normal vector j+2k.

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Q: Find a point-normal equation for the plane that is represented by the vector equation (x, y, z) =…

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Q: ii) Find the dot product of the vector a in part (i) with the displacement vector AB such that…

A: Given that  Following vectors  To find the dot product

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: 4. Find an equation (in point-normal form) of the plane containing the points K, M, and N. 5. Let R…

A: This is a problem of Vector Algebra.

Q: Write the equation of the plane with normal vector n = 11j passing through the point (12, 9, 10) in…

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Q: Expreas the unit vector dirccted toward the point (0,0, A) from arbitrary point in the plane --2. an

A: In this question, we have to find the unit vector toward the given point from the given plane the…

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: 2. A plane is defined by the equation 2x - 5y = 0. a. What is a normal vector to this plane? b.…

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Q: Find the equation for the plane through the point Po = (7,2,3) and normal to the vector n= 4i + 6j +…

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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: Let P be the plane R3 with equation x+y-2z=4. the origin (0,0,0) is not in P! find two vectors in P0…

A: Given  x+y-2 z=4      .....(1)

Q: 6. For a plane with a normal of ñ = [1,2,-9] and containing a point P (3,-4, 0), write the scalar…

A: Given: Normal of the plane π is given by, n→=i→ + 2j→-9k→ Point P on the plane is P3,-4,0 To find…

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 symmetric equations of the normal to the surface, r (u, v) = at a point (1, 1, 3

A: given ru,v=<u2,v2,u+2v> therefore ru=∂∂uu2i+∂∂uv2j+∂∂uu+2vk=2ui+0j+k…

Q: Find the equation of the plane going through the point P(2, 3, −1) with a normal vector given by n…

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Q: A particle moves on a fixed surface in F.(0), which is defined by z = 2xy. During the motion, the x…

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Q: Write the equation of the plane with normal vector n=5jn=5j passing through the point…

A: Given,

Q: Find a vector parametrization r(t) for the line with the given description. Passes through (-2, 0,…

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Q: Find Vector, Parametric and Scalar equations for the line that passes through t -2,11) and (6,1).

A: Given: - The line that passes through the points -2,11and 6,1. To find: - The parametric equations…

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

A: Topic = Vector

Q: Find a parametrization of the line in which the planes x- 2y + 2z = - 1 and – 4x+ 3y – 3z = -1…

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Q: Write the equation of the plane with normal vector n=5j passing through the point (2,10,9) in scalar…

A: Give normal vector is:

Q: Find the vectors T, N, and B at the given point. r(t) = (6 cos(t), 6sin(t), 6 In(cos(t))), (6, 0, 0)…

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Q: 285. Find the scalar equation of the plane that passes through point P(-1, 2, 1) and is…

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Q: Find an equation of the plane. The plane through the point (3, 2, 3) and with normal vector 9i + j…

A: Consider the provided question,

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: 8. Consider the following two planes: one with equation 4x – 5y + z = -2, and the other which passes…

A: Given: Given, equation of the plane, 4x- 5y +Z = -2 The other plane passing through the point (1, 1,…

Q: Find the equation for the plane through the point Po= (9,2.5) and normal to the vector n= 31 + 10j +…

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Q: A normal vector to the plane passing through the point (2, 1, -4) is (-1, 3, -61 The equation of…

A: The objective is to find the equation of plane.

Q: Find an equation for the normal plane for r(t) at the point (0, 7, –1). Find an equation for the…

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Q: 7. Consider the plane in R3 defined by 3x + y- 4z 12. a. Give a normal vector for this plane. b.…

A: In geometry and physics and its engineering applications, we use two kinds of quantities, scalars,…

Q: Determine the general equation of the plane that passes through the point P (-1,1,0) and that has a…

A: Plane passing through the point P-1, 1, 0 and has a normal vector n=2, 0, -4.

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

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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: A normal vector to the plane passing through the point (1, 3, -7) is[-2, 1, -5]. The equation of…

A: Given point is (1,3,-7) and normal vector is -2,1,-5 find the equation of a plane

Q: write the equation of the plane passing through P with normal vector n in (a) normal form and (b)…

A: The normal form of the equation of a plane P in ℝ3 is  n.x-p = 0  or  n.x = n.p where p is a…

Q: 5. Find a nonzero vector orthogonal to the plane through the points P(1,0, 1), Q(-2, 1, 3), and R(4,…

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Q: Find the equation for the plane through the point Po = (2,7,6) and normal to the vector n= 3i + 5j +…

A: Given:-normal, n=3i+5j+6kpoint on the plane, P0=2, 7, 6let (x, y , z) on the plane vector (x-2)i+…

Q: Find an equation of the plane. The plane through the point (7, 5, 4) and with normal vector 3i + j…

A: 1. Given Normal vector is 3i + j − k Let the equation of the plane in vector form is xi + yj − zk

Q: A vector orthogonal to the plane through the points P, Q and R Calculate the area of the triangle…

A: a)  The given vertices are P(-4,-4,-4), Q(0,5,-1) and R(3,1,2) PQ =0+4,5+4,-1+4 =4,9,3PR  = 3+4,…

Q: Find a vector parametrization for the line with the given description. Perpendicular to the…

A: Given points are (0,0,8). The equation of yz-plane is given by ⇒x=0 Therefore, the normal vector is…

Q: Find an equation of the plane with normal vector n =, and contains the line given by the y – 2 z - 6…

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Q: 9. Find the normal unit vector n to the surface 62 + 2y²+ 2² = 225 at the point P: (5,5, 5).

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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: Find the equation of the plane with normal vector n = 10k passing through the point (4, 3,9) in…

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Q: Find the angle between the two given planes: f = x+y+z-1, and f, =x-2y+3z-1. hint: Find the normal…

A: The angle between two planes can be easily found if we know the normal vectors to the planes.