The equation of the plane which is normal to the vector m=< -5, 11,8 > and...
Find the normal form of the equation of the plane that passes through Find the vector form of the equation of the line in ℝ2 that passes through P = (5, −2) and is parallel to the line with general equation 5x − 4y = 2.
5.) Find the equation for the plane containing the points P (5,1,4), 0 (5.312), R (1,-2,2) -- 6.) Build a parametric equations for the line tangent to the curve r(t) = 572; +(6+1); - +3K at the point P (20.-11,8)
TOTAL MARKS: 25 QUESTION 4 (a) Find a normal vector and an equation for the tangent plane to the surface at the point P: (-2,1,3). Determine the equation of the line formed by the intersection of this plane with the plane z = 0. 10 marks (b) Find the directional derivative of the function F(r, y, z)at the point P: (1,-1,-2) in the direction of the vector Give a brief interpretation of what your result means. 2y -3 [9 marks]...
a. Every matrix equation Ax b corresponds to a vector equation with the same solution set. Choose the correct answer below. O A. False. The matrix equation Ax-b does not correspond to a vector equation with the same solution set. O B. False. The matrix equation Ax b only corresponds to an inconsistent system of vector equations. O c. True. The matrix equation Ax-bis simply another notation for the vector equation x1a1 + x2a2 +·.. + xnan-b, where al ,...
In R”, find a point normal equation for the plane II which contains the line (1,1,1) + t(15, -6, -2) together with the point Q(–7, 18, –2) Answer: one such point normal equation for II is X +
(a). Find the equation of the plane through Po = (1,2,1) with normal vector i = (3,1,2) (b). Find the equation of a plane through Po = (2,3,1) and parallel to the plane P:3x + 2y -- z = 4 | Q4. Consider the line z-3 y-2 3 L, : * - - - L2: **** 2+5 y-3 -1 2 (i). Write the equations of both lines in parametric form (ii). Find the direction vectors V1, V2 of the lines...
Linear Algebra Problem 4: Given the normal vector n - 2 determine the matrix of the projection linear map through the plane (passing through the origin) which has n as a normal vector. Problem 5: Given the normal vector n = linear map through the plane (passing through the origin) which has n as a normal vector. V14' V14 V14 (#าพื้าพื้) determine the matrix of the reflection V14' V14 v14 Problem 4: Given the normal vector n - 2 determine...
Given f(x, y): 10-2x2-y, find a) The equation of the tangent plane to the surface at the point (2.2,6) b) The parametric equations of the normal line at the point (2, 2, 6) c) The outward unit normal vector to the surface at the point (2, 2,6) d) Sketch the surface and the outward unit normal vector at the point (2, 2,6). 1. Given f(x, y): 10-2x2-y, find a) The equation of the tangent plane to the surface at the...
Give the scalar equation of a plane perpendicular to the vector (8,3, 2) that contains the point (2,1, -2). Preview Points possible: 6 Unlimited attempts. Submit
Question 19 Find a normal vector of the tangent plane to 2? + y2 + x2 = 30 at the point (1, -2,5). (1,2,5) O (2,-4,-8) (-3,6,-12) None of the above or below (-2,4-10) (1,1,1)