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…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Let P. Q and R have coordinates P(1,1,2). Q(1,0,0) and R(2,1,0). (a) The line I through P and Q has vector form OP+ tv, enter the coordinates of a suitable vector v (b) Enter the coordinates of a vector that is perpendicular to the plane PQR (e) Enter the equation of the plane PQR (d) Find the line through 7(0,0,1) that is perpendicular to this plane Enter the coordinates of the point where the line k intersects the plane PQR necessary actions rather than decimals in your answer
1. Given the points P(3, 7, -5), Q(4, -9, 0) and R(6, 9, -4), determine each of the following equations and write your final answers below in the specified form. a) the equation of the line through P and Q. b) the equation of the plane through P, Q, & R. [vector] [parametric] [vector] [symmetric] [Cartesian/Scalar]
(b) Let P, be the plane in R which contains the line in R' with vector equation 6. X1 =| 5 + and the point (3, 2, 5). (This point is not on the line.) (i) A vector equation of P, is 6 X = 5 +s 4 +t 6. 6 (Use two points on the plane to find one of the direction vectors.) (ii) An equation in general form for P2 is x+ y+ To find this equation, you need a vector n = [a, b, c] which is orthogonal to the two direction vectors that you obtained in part (i).
3 4 33. Determine the vector equation, parametric equations, and, if possible, symmetric equation of the line that passes through the point P(1, 3, 5) and a. has direction vector (-2, -4, -10) b. also passes through the point Q(-7, 9, 3) c. is parallel to the line that passes through R(4, 8, -5) and S(-2, -5,9) d. is parallel to the .x-axis e. is perpendicular to the line (x, y, z) = (1, 0, 5) + (-3, 4, -6) f. is perpendicular to the plane determined by the points A(4, 2, 1), 4 2), and C(-3, 2, 1) nd 59 nsv of -3 of the plane that
Let vector a=4i-5j+3k and a point P(2,-1,3). If the length of PQ is equal to the length of vector a, and vector PQ is opposite to vector a, then the coordinate of Q is … (2,-4,0) (6,-6,0) (-2,4,0) (6,-6,-6) The equation for the plane passing through points (3,2,1),(2,1,-1), and (-1,3,2) is given as follows. 9x + y - z - 16 = 0 x + 9y - 5z - 16 = 0 x - 9y - 5z + 16 = 0 x + 5y - 9z - 16 = 0choose the correct answer

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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).