Find an equation of the plane that contains the point (-1, 2, 3) and is perpendicular to the line traced by the vector function r(t) = (-1+ 5t)i + (5 – t)j + (2 – 2t)k %3D

Q: Find the vector form of the equation of the line inR3 that passes through P = ( -1, 0, 3) and is…

A: Equation of a line passes through  x1, y1, z1 having direction ratios a, b, c is, x-x1a=y-y1b=z-z1c

Q: Find a vector normal to the plane with the given equation.9x − 4y − 11z = 2

A: Our Aim is to find a vector normal to the plane with the equation given below:-9x-4y-11x=2 -(i)

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: 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: 4 - x y + 1 %3D 2 1 3 L2 :[x, y, z] = [-2,4,3]+ t[-6, 5, 7], t E F

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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: 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: Find the equation for the plane through the point Po = (2,3,8) and normal to the vector n= 3i + 8j +…

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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, 3, 6) and with normal vector 8i + j…

A: We will solve the problem.

Q: Find both the vector equation and the parametric equations of the line through (0,0,0) that is…

A: Given vectors area. u=2,0,2w=-2,-1,0a=0,0,0 Find the vector equation of the line perpendicular to u…

Q: Find the vector equation of the line through the points P0(x0, y0, z0) and P1(x1, y1, z1).

A: P0x0, y0, z0 & P1x1, y1, z1. Now let a→ & b→ be the position vectors of the points P0x0, y0,…

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 the point A (a, a, 0) on the line y = x in the xy-plane, such that the vector AB is…

A: Solution is given below:

Q: Find a vector equation with parameter t for the line of intersection of the planes x + y + z = 4 and…

A: To find the equation of line with parameter t of the intersection of the planes  x + y + z =4 and…

Q: Find the equation for the plane through the point Po = (3,4,3) and normal to the vector n=21 + 7j +…

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Q: Find the equation of a line in vector form that is parallel to 3x−2y+z= 4, passes through the point…

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Q: (a) Prove that the planes 4.x – 2y + 6 = 0 and y – 4z – 13 = 0 intersect each other. (b) Find the…

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Q: Find a vector equation with parameter t for the line of intersection of the planes x + y + z = 3 and…

A: Given plane equations are  x + y + z = 3 and x + z = 0. We have to find the intersection line…

Q: Find a vector equation for the line segment connecting the points P = (-9,–6, 8) and Q = (-15,…

A: We have to find a vector equation for the line segment connecting the points P=-9,-6,8 and…

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

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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: Find a vector equation of the line passing through the points P(-2, 1, 3) and Q(3, 0, -2). 1+t ,te…

A: The vector equation of the line passing through the points A(x1,y1,z1) and B(x2,y2,z2)  is given by;…

Q: Find a vector normal to the plane with the given equation. 2x + 8y + 9z = 3 n =

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Q: Find an equation for the plane that passes through the point (3, -2, 1) normal to the vector n = 2i…

A: Given:A point (3, -2, 1) normal to the vector n = 2i + j + kThe normal vector can be written as,

Q: Find a vector normal to the plane -2x - 3y = 12 - 4z.

A: Given  a vector -2x-y=12-4z. We need to find the vector normal to the plane.

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: Find a vector equation for the line through the point (2, 5, 8) perpendicular to the plane 2x + 5y +…

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Q: Find the equation of the plane that passes through the point P(1, 0, 2) and contains the line whose…

A: Hi there, At a time we can answer only one question. So, I have answered first one (#6).

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: Q2: Determined the component of the vectors at each point…

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Q: E. Find an equation of the plane passing through the point (6, 3, 5) and containing the line of…

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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 the linear equation of the plane through the point (-3, 4, 3) and perpendicular to the line…

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Q: Find parametric equations for the line through the point P(-5,6,7) and perpendicular to the vectors…

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Q: 4

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Q: Find a vector that gives the direction of maximum rate of increase for the 6xyz at (-1,2,1) (a)6(2i…

A: To find A vector that gives the direction of maximum rate of increase.

Q: Find a vector equation with parameter t for the line of intersection of the planes x + y + z = 4 and…

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Q: Find the vector equation of the line that is perpindicular to the line q(t) = (1,2, 3) + s(2, –1, 1)…

A: Consider a point P(1+2s, 2-s, 3+s) on the vector equation of the line. The vector joining points P…

Q: Find an equation of the line that goes through A(0, 1, 4) and is orthogonal to the Y-axis and vector…

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Q: Find a vector equation for the line that goes through the points (5,9,0) and (0, 11, 1). F(1) = with…

A: A ( 5,9,0) B ( 0,11,1)

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 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: Determine a vector equation of the line passing through (6, 0, 3) and parallel to the line of…

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

A: Answer

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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