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Kjell, Chapter 5
What is the direction of the vector represented by (5,-5)T
True or False: The formula for the direction of a 2D vector is:
angle of (x, y)T = arc tan( y/x )
What is the direction of the vector represented by (5,-5)T
What is the direction of the vector represented by (-5,-5)T
A vector has a length of 4 and an orientation of 150 degrees. Which of the following transpose matrices properly describes the vector?
True or False: 2*pi radians = 180 degrees
where the asterisk indicates multiplication and pi is the constant that begins with 3.14159
What is the meaning of the following two images?
These images were inserted here simply to insert some space between the questions and the answers to keep them from being visible on the screen at thesame time.
This image was also inserted for the purpose of inserting space between the questions and the answers.
False. There are 2*pi radians in a full circle, so
2*pi radians = 360 degrees
A. (-3.464,2.0)T
Kjell, Chapter 5
D. -135 degrees
Kjell, Chapter 5
C. -45 degrees
Kjell, Chapter 5
True. Arc tan( z ) means "find the angle that has a tangent of z." When you do this with a calculator, remember that the answer may be in radians or in degrees. Some calculators give you the option of using use either format.
Kjell, Chapter 5
C. 315 degrees, or
D.-45 degrees
depending on the convention in use.
Kjell, Chapter 5
True
Kjell, Chapter 5
False. If v is a vector, then -v is a vector pointing in the opposite direction.
Kjell, Chapter 4.
False. It is possible for the sum of the squared elements to be equal without the elements themselves being equal. In that case, the lengths are the same but the directions are not the same.
Kjell, Chapter 4.
True. Since corresponding elements must be equal, so corresponding squares must be equal, so the sum must be equal, so the length must be equal.
Kjell, Chapter 4
False. The length property of a vector must be zero or positive. It cannot be negative.
Kjell, Chapter 4.
True
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C. 6
Kjell, Chapter 4
False. The correct statement follows where |(x,y,z)T| represents a three-dimensional vector:
|(x,y,z)T| = sqrt(x^2 + y^2 + z^2)
Kjell, Chapter 4
True
Kjell, Chapter 4
False. The following statement is true where the left angle bracket followed by the equal sign indicates "less than orequal." This is known as the "triangle inequality."
|u + v| is less than or equal |u| + |v|
(Note that there is a problem with displaying the left angle bracket using my xhtml to cnxml converter program. That is why it is spelled out in theabove statement.)
Kjell, Chapter 4
C. 5
Kjell, Chapter 4
C. 5
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C. 10
Kjell, Chapter 4
C. 4
The length of the vector is 4 units.
Kjell, Chapter 4
False. The correct statement is:
When a 2D vector is aligned with the y axis, the column matrix that represents it has a non-zero value in the second element, and zero for the firstelement.
Kjell, Chapter 4
True. as in (3,0)T
Kjell, Chapter 4
B. 3
The length of the vector is 3 units.
Kjell, Chapter 4
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