FunctFind the point at which the line intersects the given plane.Symb-x = 4 – 4t, y = 5t,z = 1 + t;x + 2y - z = 8Relatic(x, y, z) =Setso!VectorsNeed Help?Read ItTrig

We have to find the point at which the line intersects the given plane.

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Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.1: Parabolas

Problem 37E

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In these exercises we find the area of plane figures. Plot the points P(5,1),Q(0,6) and R(5,1) on a coordinate plane. Where must the point S be located so that the quadrilateral PQRS is a square? Find the area of this square.
Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?
aWhat is a vector in the plane? How do we represent a vector in the coordinate plane? bFind the vector with initial point (2,3) and terminal point (4,10). cLet v=2,1. If the initial point v is placed at P(1,1), where is its terminal point? Sketch several representations of v. dHow is the magnitude of v=a1,a2 defined? Find the magnitude of w=3,4. eWhat are the vectors i and j? Express the vector v=5,9 in terms of i and j. fLet v=a1,a2 be a vector in the coordinate plane. What is meant by the direction of v? What are the coordinates of v in terms of its length and direction? Sketch a figure to illustrate your answer. gSuppose that v has length |v|=5 and direction =/6. Express v in terms of its coordinates.
Parameterize the plane that contains the three points (−1,3,2), (12,12,−8), and (30,15,40). r(s,t)=______? (Use s and t for the parameters in your parameterization)
Find the coordinates of the point. The point is located in the yz-plane, seven units to the right of the xz-plane, and eight units above the xy-plane. (x, y, z) =
(a)Find the angle between the line r=i+2j-k+gamma(i-j+k) and the plane r.(2i-j+k)=4 (b) Find the equation of a plane containing the line of intersection of the planes x+y+z=6 and 2x+3y+4z+5=0
(a) Find the point at which the given lines intersect. r = 3, 2, 0 + t 2, −2, 3 r = 5, 0, 3 + s −2, 2, 0 (x, y, z) = (b) Find an equation of the plane that contains these lines.
22. a) Determine the equation of the line of intersection of planes 1 and 2. Express your answer in the form: [x,y,z] = [x0,y0, 0] + t[a, b, 1], b) Find the point where the line crosses the xz- plane. ?1: 2? + 2? − 3? + 7 = 0 ① ?2: 4? + 7? − 5? + 11 = 0 ②
Let r be the straight line that passes through the point A(3,6,4), intersects the z axis and is parallel to the plane π:3x+4y+z=9. Mark the alternative that corresponds to the point of intersection of the line r with the xy plane. a. (29/11, 24/11, 0) b. (0, 0, 37) c. (38/11, 72/11, 0) d. (37/11, 74/11, 0) e. (37, 74, 0)
(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.

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Find the point at which the line intersects the given plane. x = 4 – 4t, y = 5t, z = 1 + t; x + 2y - z 8 (x, y, z) =