15-20 . Equations of Planes A plane has normal vector n andpasses through the point P. (a) Find an equation for the plane.(b) Find the intercepts, and sketch a graph of the plane.15. n 3D (1, 1, —1), Р(0, 2, —3)16. n 3 (3, 2, 0), Р(1,2, 7)17. n = (3, 0, –). P(2, 4, 8)18. n = (. -4. -1) P(6,0, 3)19. n = 3i – j+ 2k, P(0, 2, –3)20. n = i + 4j, P(1,0, -9)

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Answered: 15-20 . Equations of Planes A plane has…

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Vectors In Two And Three Dimensions

Section9.6: Equations Of Lines And Planes

Problem 15E

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(5.1) Find the vector form of the equation of the plane that passes through the point P0 = (1, −2, 3) and has normal vector ~n =< 3, 1, −1 >. (5.2) Find an equation for the plane that contains the line x = −1 + 3t, y = 5 + 3t, z = 2 + t and is parallel to the line of intersection of the planes x −2(y −1) + 3z = −1 and y = −2x −1 = 0.
finding vector and equition of a line (a) Find the vector form of the equation of the plane that passes through the point P0 = (1, −2, 3) and has normal vector ~n =< 3, 1, −1 >. (b) Find an equation for the plane that contains the line x = −1 + 3t, y = 5 + 3t, z = 2 + t and is parallel to the line of intersection of the planes x −2(y −1) + 3z = −1 and y = −2x −1 = 0.
2.2(3) Please help me answer and show your work on this question. A plane has as a normal vector n = [2,-1,-3] and passes through point A(1, -1, 2). A) Determines the Cartesian equation of the plane. B) Determines parametric equations of the plane.
(a) Find a vector perpendicular to the plane that contains the points P(1, 0, 0), Q(2, 0, −1), and R(1, 2, 4). (b) Find an equation for the plane that contains P, Q, and R. (Let x, y, and z denote the standard coordinate variables.) (c) Find the area of triangle PQR.
SOLVE the letters in black 7. The planes 3x + 6z = 1 and 2x + 2y - z = 3 intersect in a line. i. Show that the planes are orthogonal ii. Determine the equations of the connecting line of the planes. Find the distance from point P(1,4,0) to the plane through A(0,0,0), B(2,0, -1) and C(2, -1,0) Find the vector parallel to the 2x - y - z = 4 plane and orthogonal to i + j + k )
The solution set to the linear equation 5⋅x−y+3⋅z=1 is a plane in 3 dimensions. Write down a normal vector to the plane :n = Write down the coordinates of one point p in the plane;p= vectors v and w are orthogonal to n. Find their x-coordinates: v=( ? , 1,0) interpreted as (( , 1,0)1,0) w =( ? , 0,1) interpreted as (( , 0,1)
(a) find an equation of the plane that passes through the points A(2,1,1) B(-1,-1,10) C(1.3.-4).(b) Find symmetric equations for the line through B that is perpendicular to the plane in part (a)(c) A second plane passes through (2,0,4) and has normal vector (2,-4,-3). Show that the acute angle between the planes is approximately 43 degree.(d) Find parametric equations for the line for the line of intersection of the two planes.
4. Plane passing through point P0 (1, 2, 1) and perpendicular to vector (1, -1, 2)Find the equation (D1). Also, from the points P1 (1, 0,0), P2 (0, 2, 0) and P3 (0, 0, -1)Write the passing plane equation (D2). If these planes (D1 and D2) haveFind its intersection.
consider the point A = (-5, -3, 7) and the vector n = <1, 1, 1>a) Which coordinate plane (the x-y plane, the y-z plane, or the x-z plane) is this point closest to, andhow close is it to that plane?b) How far from the origin is the point A?c) Find the equation of the plane that contains point A and has normal vector n. I keep coming up with the wrong answers for this.
Consider the plane that passes through the point P ( 0 , 4 , 0 ) and contains the vectors ⟨ 2 , 0 , 1 ⟩ and ⟨ − 1 , 0 , 1 ⟩ .Find the equation of this plane. Show your work to find the information you need for this equation.Then draw a picture that clearly shows the plane, the point, the two vectors given, and the normal vector for the plane.
3D Cartesian vectors Use the right hand method to draw a 3-D Cartesian plane with three labelled axes Also, using the plane, you have drawn draw a vector with its tail at the origin and it’s had a point P (1,-6,4) Determine the magnitude of the vector
1.Find the distance between the point (-3, 1) and the line y = -4/3 x - 4/32.Let u = (3, 4) and v = (4, 2). Find the projection of v onto u3.What is the normal vector of the plane x + y - z = 1?4.The vector u = (6, 1, 4) is orthogonal to

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