Determine the vector, parametric, and scalar equations of the plane for each ofthe following situations:ond11910613101 sl(a)the plane through the point (4,-1,1) with direction vectors (3, -2, 7) and(0, 1, -2).The plane through the points P(1, -3, 2), Q(0, 1, 2), and R(9, 2, 0).(b)

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Answered: he vector, parametric, and scalar…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 31E

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Find the equation of the plane in xyz-space through the point P=(3,3,2) and perpendicular to the vector n=(−2,1,5).
1.Find an equation of the plane which passes through the point (2, -7, 1) and is perpendicular to 3x - y -11z =0.2.Find the distance between the parallel planes 2x - y - z = 5 and -4x + 2y + 2z = 123.What is the normal vector of the plane x + y - z = 1?
The scalar equation of the plane with normal vector [4, -1, 9] and passing through the point (2, -1, -1) is: a. 4x - y + 9z = 0 b. 4x - y + 9z + 7 = 0 c. 4x + y + 9z = 0 d. 4x - y - 9z = 0
Find vector and parametric equations of the plane that contains the point P = (−3, 1, 0) and is parallel to the two vectors v1 = (0, −3, 6) and v2 = (−5, 1, 2).
1. Determine the scalar equation of a plane with normal vector n = [3,1,3] that has a y-intercept of 5.
(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.
Determine the general equation of the plane that passes through the point P (-1,1,0) and that has a normal vector n = (2,0, -4).
Find an equation of the plane. The plane through the point (3, 2, 3) and with normal vector 9i + j − k
Find the equation of the plane containing the points P = (−1, 3, 2),Q = (−5, 1, 1), and R = (6, 0, −3) by first finding two vectors in the plane and avector perpendicular to the plane
Find a vector that is orthogonal to the plane containing the points p(3,1,1) ,Q (4,-2,1) , and R( 5,2,-1) .
Determine the scalar, vector and parametric equations of the plane that passes through thepoints (3,2,5), (0,-2,2) and (1,3,1).

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he vector, parametric, and scalar equations of the plane for each of g situations: 1961 301 il bari plane through the point (4,-1,1) with direction vectors (3, -2, 7) and -, -2). plane through the points P(1, -3, 2), Q(0, 1, 2), and R(9, 2, 0).