Find the volume of the parallelepiped defined by the vectorsй 3 (3, —1,4), i — (2, 1, —2) and й — (5, 0, —1).А. 14В.15С. 16D. 17

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Answered: Find the volume of the parallelepiped…

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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1. Given the vectors à = (-1, 1, 1), b = (2, 1, –3), and ở = (5, 1, –-7), calculate the value of each of the following: a. d xB b. Bx 2 à-(5 x a) (a x 8) × (5 x 2) с. а d.
For what value(s) of k are the vectors ü (2k, 5, k) and v = (3,-8, k) perpendicular?
1. A line passes through the points A(2, 3) and B(-2, 1). Find a vector equation of the line. [x, y] = [-4, -2] + 12, 3] [x, yl = [2, 3] + 41-4,-2] [x, y) = [2, 3] + 1-2, 1] A В D 2. A line has slope 3 and y-intereept 5. Find a vector equation of the line. [x, y] = [1, -3] + [0, 5) [x, yl =[-3, 5] + -3, -31 [x, y] = [0, 5] + [1, –3] [x, yl - [5, 0j + j0, –31 A B _ 3. The Cartesian cquation of the plane with normal vector - [1, 2, 1] and passing through the point (3, 2, 1) is: x+ 2y +z+ 8 = 0 x+ 2y + z- 8 - 0 3x + 2y +z-8 =0 3x + 2y +z+8 = 0 A B D _ 4. The equation of a plane is [x, y, z] = [3, 1, 3] + s[=1, 1, 2] + [2, 1, 1]. Find a normal vector to the plane. [3, 1, 3] [-1, 5, -3] [-1, 1, 2] [2, 1, 1] A В D 5. The equation of a plane is x+ 2y+ 3z- 6 = 0. Find the y-intereept of the plane. -1 C 3 В 2 D -3 _ 6. Two planes are parallel if their normals are perpendicular are collincar dot product is zero are different в D 7. Which of the following determines a plane? A a line and a point…
multivariable calculus problem
12 If a. x and y are three non-zero and mutually non-parallel vectors, and the vectors b and e are given by b=x-(x-â)â and c=y-(y â)â-(y.b)b, where â and b are unit vectors along a and b respectively, show that a, b and c are mutually perpendicular.
Find the volume of the parallelepiped determined by the vectors a, b, and c. a = 4, 2, −3 , b = 0, 3, 2 , c = 4, −3, 5 cubic units
Calculate the area of the parallelogram spanned by the vectors and .the⃗ ( 3 ; - 3 ; 1 )a→(3;−3;1) b⃗ ( 4 ; 9 ; 2 )b→(4;9;2)
17. The sum to two unit vectors is a unit vector. The magnitude of the difference of the two unit vectors is: (A) V2 (B) V3 (C) V5 (D) 2
33. Find the direction and magnitude of the vectors. a. A = (5.0 m) x + (-2.0 m) y, →>> →>> b. B = (-2.0m) x + (5.0 m) y, and (c) A + B. → a. A = (22 m) x + (-14 m) y, b. B = (2.5 m) x + (13 m) ỹ, and (c) A + B. • For the vectors given in Problem 34, express (a) A – B and (b) B – A in unit vector notation.

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Find the volume of the parallelepiped defined by the vectors й%3 (3, —1,4), ѣ —D (2, 1, —2) and й %3 (5, 0, —1). А. 14 В. 15 С. 16 D. 17