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. 7x + 2y + 5 Z=4 4

Q: Find a unit norm vector that is orthogonal to both the vector (1,2, –1) and the line of intersection…

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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: 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: 2. The plane containing the point P(Xg» Yor Zo) and having the normal vector n = (a, b, c) is…

A: Equation of a plane passing through the point Px0, y0, z0 and perpendicular to the vector n=a, b, c…

Q: Find an equation of the plane that passes through the point P(4, 7, 1) and has the vector n = (1, 3,…

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Q: What is equation of the plane passing through the point A(-2, –1, –3) and parallel to the vectors ā…

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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, 9, 6) and with normal vector 7i + j –…

A: Find an equation of the plane

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

A: We have to find the equation of plane passing through point A(2,1,3) and parallel to vectors…

Q: Find an equation of the plane that passes through the point P(4, 6, 3) and has the vector n = (1,6,…

A: I have stated the used formula in the solution.

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

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Q: Find the equation of the plane E passing through the point P(2,3,1) and parallel to the vectors K =…

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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 the scalar equation for the plane passing through the points P-(-1. 5.-1. P=(-1, 6, 5), and…

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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: Find a scalar equation for the plane that contains the points P, Q and R

A: We know that equation of plane passing through three points A(x1,y1,z1),B(x2,y2,z2), C(x3,y3,z3)  is…

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: 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: The equation of the plane that passes through the point P(1,0,0) and has the vector n = (0,0, 1) as…

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Q: Find the vector parametric equation of the line that passes through the points P(6,–2, –1) and…

A: The vector equation of a line is  . Where represent the position vector,  represent the direction…

Q: Consider the vector y = [1 2 3]. Find the orthogonal projection of y onto the plane x, - 2x2 + 4x3 =…

A: Given vector is y=1,2,3 Given plane is x1-2x2+4x3=0 Normal vector to the p[lane is n=1,-2,4…

Q: Find a vector tangent to the curve of intersection of the two cyclinders ? + y² = 98 and y² + z² =…

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Q: Find an equation of the plane containing the point P(2,1, –1) and having the normal vector N = -î+3…

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Q: In Exercises 1-8, write the equation of the plane with normal vector npassing through the given…

A: Given  n = i-k, (4,2,-8)

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: Determine any three points on the plane given by 5x - 6y + 10z - 15  = 0. Using these points, give a…

A: The given plane is: 5x - 6y + 10z - 15  = 0. We have to find any three points on the plane. Using…

Q: In Exercises 1-8, write the equation of the plane with normal vector npassing through the given…

A: Given,  n = k, ( 6, 7, 2) To find  the equation of the plane with normal vector npassing through the…

Q: Find the scalar equation for the plane passing through the points P1(2, 1, 5), P2(2, 0, 9), and…

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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: 1. Show that A(r - ro) + B(y - yo) =0 is an equation for the line in the ry-plane through the point…

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

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Q: Find a scalar equation of the plane that passes through the points (1, 1, 1) and (2,0,3) and is…

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

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Q: In Exercises 1-8, write the equation of the plane with normal vector npassing through the given…

A: Our Aim is to write the equation of the plane with normal vector n⇀=(-1,2,1) passing through the…

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 an equation of the plane that passes through the point P(3, 5, 1) and has the vector n = (1, 8,…

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

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: Find the scalar equation of the plane that passes through point P(−3, 3, 5) and is perpendicular to…

A: To Find: Scalar equation of the plane that passes through point P(−3, 3, 5) and is perpendicular to…

Q: Find an equation of the plane that passes through the point P(4, 5, 3) and has the vector n = (1, 8,…

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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: 2. Determine the vector equation of the plane that contains the following two lines. L1: 7 = [ 4,…

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