If |(3d + b) x (a + b)| = 24, then the area of the parallelogram determined by d and b is O A. 4 O B. 6 С. 12 D. 3 O E. 8

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 17EQ
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Minimize and Maximize f(x,y,z) = (x + 1)² + (y + 1)2 + (z+ 1)?
subject to the constraint x2 + y2 + z² – 27 = 0 to get
(A) (3,3,3) is the point on f(x, y, z) = (x + 1)² + (y + 1)² + (z + 1)² farthest from
(0,0, v27), and (-3, –3,–3) is the point that is closest
%3D
(B) (0,0, v27) is the point on the sphere x2 + y2 + z? = 27 closest to the point
(-1,–1,–1), and (0,0,-V27) is the point that is farthest.
II
(C) (3,3,3) is the point on f (x, y, z) = (x + 1)² + (y + 1)² + (z + 1)²farthest from
(0,0, v27), and (-3,–3,–3) is the point that is closest.
%3D
(D) (3,3,3) is the point on the sphere x2 + y2 +z² = 27 closest to (-1,-1,-1), and
(-3,-3,-3) is the point that is farthest.
(E) (3,3,3) is the point on the sphere x2 +y2 + z² = 27 farthest from the point
(-1,–1,–1), and (-3,-3,-3) is the point that is closest.
%3D
Transcribed Image Text:Minimize and Maximize f(x,y,z) = (x + 1)² + (y + 1)2 + (z+ 1)? subject to the constraint x2 + y2 + z² – 27 = 0 to get (A) (3,3,3) is the point on f(x, y, z) = (x + 1)² + (y + 1)² + (z + 1)² farthest from (0,0, v27), and (-3, –3,–3) is the point that is closest %3D (B) (0,0, v27) is the point on the sphere x2 + y2 + z? = 27 closest to the point (-1,–1,–1), and (0,0,-V27) is the point that is farthest. II (C) (3,3,3) is the point on f (x, y, z) = (x + 1)² + (y + 1)² + (z + 1)²farthest from (0,0, v27), and (-3,–3,–3) is the point that is closest. %3D (D) (3,3,3) is the point on the sphere x2 + y2 +z² = 27 closest to (-1,-1,-1), and (-3,-3,-3) is the point that is farthest. (E) (3,3,3) is the point on the sphere x2 +y2 + z² = 27 farthest from the point (-1,–1,–1), and (-3,-3,-3) is the point that is closest. %3D
If |(3a + b) x (a + b)|
24, then the area of the parallelogram determined by a and b is
O A. 4
О В.6
С. 12
D. 3
O E. 8
Transcribed Image Text:If |(3a + b) x (a + b)| 24, then the area of the parallelogram determined by a and b is O A. 4 О В.6 С. 12 D. 3 O E. 8
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