14. Deand y as the vectors x = [1, 3, 5.7,9] and y = [2, 5, 8, 11, 14. Then use them in the following expressions to calculate z using element-by-clement calculations. (a) z= (b) = = x(x -y)-(x-y)
14. Deand y as the vectors x = [1, 3, 5.7,9] and y = [2, 5, 8, 11, 14. Then use them in the following expressions to calculate z using element-by-clement calculations. (a) z= (b) = = x(x -y)-(x-y)
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...
Related questions
Question
![Tements thal are
squares of the elements
of the original vector. Then use MATLAB built-in functions sum and
sgrt to calculate the length. All of these steps can be written in one com-
mand.
9. The unit vector u, in the direction of the vector u = xi + yj +zk is given by
u, = 1+ vj +:k
+ y +
u = - 8i – 14j + 25k by writing one MATLAB command.
Determine the unit vector of the vector
10. The following two vectors are defined in MATLAB:
v = [3, -2, 4] u= (5,3, -1]
By hand (pencil and paper) write what will be displayed if the following com-
mands are executed by MATLAB. Check your answers by executing the com-
mands with MATLAB.
(a) v. *u
(b) v*u'
(c) v'*u
I1. Two vectors are given:
u = -3i + 8j - 2k and v = 6.5i-5j-4k
Use MATLAB to calculate the dot product u v of the vectors in three ways:
(a) Write an expression using element-by-element calculation and the MAT-
LAB built-in function sum.
(b) Define u as a row vector and v as a column vector, and then use matrix
multiplication.
(c) Use the MATLAB built-in function dot.
3.9 Problems
89
12. Define the vector v = [2 4 68 10]. Then use the vector in a mathematical
expression to create the following vectors:
! ! ! ! 11
(b) b = 411
(d) d = [1 111 1]
(a) a =
(c) e = [1 23 4 s)
13. Define the vector v = [5 4 3 2 1]. Then use the vector in a mathematical
expression to create the following vectors:
(a) a = [52 42 32 22 12]
(c) e = [25 20 15 10 5]
(b) b = [55 44 33 22 1
(d) d = [4 3 2 i o]
14. De and y as the vectors x = [1, 3, 5. 7. 9] and y = [2, 5, 8, 11, 14. Then
use them in the following expressions to calculate z using element-by-element
calculations.
(a) :=
x+ y
(b) : = x(x -y)-(x-y)
15. Define p and w as scalars, p = 2.3 and define w = 5.67, and, t, x, and y as the
vectors t= [1,2, 3, 4, 5), x= [2.8,2.5, 2.2, 1.9, 1.6], and y= [4,7, 10, 13, 17].
Then use these variables to calculate the following expressions using element-
by-element calculations for the vectors.
(a) T= elx + y)
(b) S = e(x+ y) wxt
py
16. The area of the parallelogram shown can be cal-
culated by ra xrad. Use the following steps
in a script file to calculate the area:
Define the position of points A, B, and C as vec-
tors A = [2, 0], B = [10,3]. and C = [4, 6].
Determine the vectors r and re from the
C (4, 6)
B(10, 3)
A (2, 0)
points.
Determine the area by using MATLAB's built-in functions cross, sum, and
sqrt.
sqrt.
17. Define the vectors:
u = - 2i + 6j + 5k, v = 5i - lj + 3k, and w = 4i + 7j - 2k
%3D
Use the vectors to verify the identity:
u x (v xw) = v(u w) - w(u- v)
Using MATLAB's built-in functions cross and abs, calculate the value of
the left and right sides of the identity.
90
Chapter 3: Mathematical Operations with Arrays
18. The dot product can be useu Tor uerer ng the](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F92b90703-0398-4d46-80d6-ba1c73cd4d64%2F9b2c05e2-81a0-480d-8e3a-168f76bd4e50%2Fna2qal_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Tements thal are
squares of the elements
of the original vector. Then use MATLAB built-in functions sum and
sgrt to calculate the length. All of these steps can be written in one com-
mand.
9. The unit vector u, in the direction of the vector u = xi + yj +zk is given by
u, = 1+ vj +:k
+ y +
u = - 8i – 14j + 25k by writing one MATLAB command.
Determine the unit vector of the vector
10. The following two vectors are defined in MATLAB:
v = [3, -2, 4] u= (5,3, -1]
By hand (pencil and paper) write what will be displayed if the following com-
mands are executed by MATLAB. Check your answers by executing the com-
mands with MATLAB.
(a) v. *u
(b) v*u'
(c) v'*u
I1. Two vectors are given:
u = -3i + 8j - 2k and v = 6.5i-5j-4k
Use MATLAB to calculate the dot product u v of the vectors in three ways:
(a) Write an expression using element-by-element calculation and the MAT-
LAB built-in function sum.
(b) Define u as a row vector and v as a column vector, and then use matrix
multiplication.
(c) Use the MATLAB built-in function dot.
3.9 Problems
89
12. Define the vector v = [2 4 68 10]. Then use the vector in a mathematical
expression to create the following vectors:
! ! ! ! 11
(b) b = 411
(d) d = [1 111 1]
(a) a =
(c) e = [1 23 4 s)
13. Define the vector v = [5 4 3 2 1]. Then use the vector in a mathematical
expression to create the following vectors:
(a) a = [52 42 32 22 12]
(c) e = [25 20 15 10 5]
(b) b = [55 44 33 22 1
(d) d = [4 3 2 i o]
14. De and y as the vectors x = [1, 3, 5. 7. 9] and y = [2, 5, 8, 11, 14. Then
use them in the following expressions to calculate z using element-by-element
calculations.
(a) :=
x+ y
(b) : = x(x -y)-(x-y)
15. Define p and w as scalars, p = 2.3 and define w = 5.67, and, t, x, and y as the
vectors t= [1,2, 3, 4, 5), x= [2.8,2.5, 2.2, 1.9, 1.6], and y= [4,7, 10, 13, 17].
Then use these variables to calculate the following expressions using element-
by-element calculations for the vectors.
(a) T= elx + y)
(b) S = e(x+ y) wxt
py
16. The area of the parallelogram shown can be cal-
culated by ra xrad. Use the following steps
in a script file to calculate the area:
Define the position of points A, B, and C as vec-
tors A = [2, 0], B = [10,3]. and C = [4, 6].
Determine the vectors r and re from the
C (4, 6)
B(10, 3)
A (2, 0)
points.
Determine the area by using MATLAB's built-in functions cross, sum, and
sqrt.
sqrt.
17. Define the vectors:
u = - 2i + 6j + 5k, v = 5i - lj + 3k, and w = 4i + 7j - 2k
%3D
Use the vectors to verify the identity:
u x (v xw) = v(u w) - w(u- v)
Using MATLAB's built-in functions cross and abs, calculate the value of
the left and right sides of the identity.
90
Chapter 3: Mathematical Operations with Arrays
18. The dot product can be useu Tor uerer ng the
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