Question 8 An equation of the plane passing through the points A(1,2,3), B(2, 3, 1), C'(3, 1, 2) is(a) x – y+ z = 2 (b) x +y - z = 0 (c) x+ y + z = 6(d) x - y – z = 0(e) none of the aboveQuestion 9 If u and v are perpendicular vectors in R' and ||u|| = 2, ||v|| = 3, then ||u x (v + u)|| =(a) 6 (b) 12 (c) 10 (d) 0 (e) none of the above

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Answered: Question 8 An equation of the plane…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section: Chapter Questions

Problem 24RE

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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.
1. Find a vector equation of the plane containing the points ?(2, 0, −1), ?(3, 4, 0), and ?(4, −1, 1).
Find the equation of the plane passing through the point (2,−1, 3) and normal to the vector N = (2, 3, 4)T .
1.Let u = (-4, 3) and v = (6, -1). What is the orthogonal projection of u onto v?2.Let u = (3, 1, -7) and v = (1, 0, 5). What is the orthogonal projection of u onto v?3.Let u = (-4, 3) and v = (6, -1). What is the vector component of u orthogonal to v?4.Find the distance between the point (3, 1, -2) and the plane x + 2y - 2z = 4.
Find the equation of the plane passing through the point (3, 2, 2) perpendicular to the vector n=2i+3j-k.
Which of the following are equations for the plane through the points P(1, 1, -1), Q(3, 0, 2), and R(-2, 1, 0)? a. (2i - 3j + 3k) # ((x + 2)i + (y - 1)j + zk) = 0 b. x = 3 - t, y =-11t, z = 2 - 3t c. (x + 2) + 11(y - 1) = 3z d. (2i - 3j + 3k) * ((x + 2)i + ( y - 1)j + zk) = 0 e. (2i - j + 3k) * (-3i + k) # ((x + 2)i + ( y - 1)j + zk) =0
A particle starts at the point P=(-3,3,4) when t=0 and moves along a straight line toward Q=(-1,7,6) at a speed of 7cm/sec. Let x, y, and z be measured in cm, and t in seconds. Find a parametric vector equation for the position of the object. r(t)=?

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Question 8 An equation of the plane passing through the points A(1,2,3), B(2, 3, 1), C(3, 1,2) is (a) r – y + z = 2 (b) x +y- z = 0 (c) r+y+z = 6 (d) r - y – z = 0 (e) none of the above