1. Which of the following is true about 2 equal vectors u and v in R?I. u and v have the same initial point and same length.II. u and v have the same terminal point and same length.III. u and v have the same length and direction.A. I only B. II only C. III only D. Both I & IIE. None of these2. If u = cos(kx) cosh(2y) is harmonic, which of these can be the value of k?%3DВ. -2C. +2E. None of theseA. 2D. +43. Which of these is true about the function f(z) =?22+1A. It is nowhere analytic.B. It is analytic everywhere except at z = i.C. It is analytic everywhere except at z = -i.D. It is analytic everywhere except at z = ti.E. It is analytic everywhere except at z = 0.4. Which of these is the resultant of the vectors (-11,12,-21) and(11,12, 21)?A. 24iВ. 24)C. 24kD. 0E. None of these5. The region described by z - 1+ il s 1 isA. A circle in the first quadrant.B. A disc in the second quadrant.C. A circle in the third quadrant.D. A disc in the fourth quadrant.E. An annulus.

As per the company guidelines we can solve first question. I hope that the given solution will help…

1. Which of the following is true about 2 equal vectors u and v in R? I. u and v have the same initial point and same length. II. u and v have the same terminal point and same length. III. u and v have the same length and direction. A. I only B. II only C. III only D. Both I & II E. None of these

1. Which of the following is true about 2 equal vectors u and v in R? I. u and v have the same initial point and same length. II. u and v have the same terminal point and same length. III. u and v have the same length and direction. A. I only B. II only C. III only D. Both I & II E. None of these

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter1: Vectors

Section1.3: Lines And Planes

Problem 8AEXP

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Question

1. Which of the following is true about 2 equal vectors u and v in R?
I. u and v have the same initial point and same length.
II. u and v have the same terminal point and same length.
III. u and v have the same length and direction.
A. I only B. II only C. III only D. Both I & II
E. None of these
2. If u = cos(kx) cosh(2y) is harmonic, which of these can be the value of k?
%3D
В. -2
C. +2
E. None of these
A. 2
D. +4
3. Which of these is true about the function f(z) =?
22+1
A. It is nowhere analytic.
B. It is analytic everywhere except at z = i.
C. It is analytic everywhere except at z = -i.
D. It is analytic everywhere except at z = ti.
E. It is analytic everywhere except at z = 0.
4. Which of these is the resultant of the vectors (-11,12,-21) and
(11,12, 21)?
A. 24i
В. 24)
C. 24k
D. 0
E. None of these
5. The region described by z - 1+ il s 1 is
A. A circle in the first quadrant.
B. A disc in the second quadrant.
C. A circle in the third quadrant.
D. A disc in the fourth quadrant.
E. An annulus.

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