Three vectors are defined by position vectors defined m=(5,4,2), n=(-1,-3,6) and p=(x,-y,-z), where x, y, z represent the last three digits of your index number. Calculate the following:- i) vector (2m+ 3ñ– 4p) ii) a vector F with magnitude F = 2 which acts in the direction opposite F

Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Vectors In Two And Three Dimensions
Section9.CR: Chapter Review
Problem 8CC
icon
Related questions
Topic Video
Question
100%
last three digits of index number -071.
QUESTION 1.
a)
Three vectors are defined by position vectors defined m=
n=(-1,-3,6) and p=(x-y,-z), where x, y, z represent the last
three digits of your index number. Calculate the following:-
i)
vector (2m+3ñ-4 p
ii)
a vector F with magnitude F = 2 which acts in the
direction opposite F
b)
Given two vectors P=-xi + yj – zk , where x, y, z represent
the last three digits of your index number and Q= 41 – 2j+ 3k .
Calculate the following:-
i)
ii)
angle 0, the angle between vectors P and Q using the
dot product formula.
c)
Given a potential function f = Ax y z + Bxz² – Cxy, where the
coefficients A, B,C , are the last three digits of your index number,
find the following:-
i)
conservative vector field F.
ii)
Divergence, DivF
iii)
Divergence at the cross sectional point P=(1,1,1) and
interpret your answer.
d)
Use line integral method to evaluate F(x, y)• dr ,where
R
F(x, y) =-
1
(3x² y7+ 4xy j) and M, N, K are the last three
М+N+ K
digits of your index number and Ris bounded by the
curves y= x´ and y= x.
Transcribed Image Text:QUESTION 1. a) Three vectors are defined by position vectors defined m= n=(-1,-3,6) and p=(x-y,-z), where x, y, z represent the last three digits of your index number. Calculate the following:- i) vector (2m+3ñ-4 p ii) a vector F with magnitude F = 2 which acts in the direction opposite F b) Given two vectors P=-xi + yj – zk , where x, y, z represent the last three digits of your index number and Q= 41 – 2j+ 3k . Calculate the following:- i) ii) angle 0, the angle between vectors P and Q using the dot product formula. c) Given a potential function f = Ax y z + Bxz² – Cxy, where the coefficients A, B,C , are the last three digits of your index number, find the following:- i) conservative vector field F. ii) Divergence, DivF iii) Divergence at the cross sectional point P=(1,1,1) and interpret your answer. d) Use line integral method to evaluate F(x, y)• dr ,where R F(x, y) =- 1 (3x² y7+ 4xy j) and M, N, K are the last three М+N+ K digits of your index number and Ris bounded by the curves y= x´ and y= x.
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Knowledge Booster
Algebraic Operations
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning