What Happens to the Magnitude of a Vector When Rotated?

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In summary, the first question is asking about the magnitude of a vector that has been rotated 60 degrees counter-clockwise from its original direction of 30 degrees. The possible answers suggest that the magnitude may either increase or decrease, but the correct answer is not explicitly given. In the second question, the components of a vector are given and the question asks for the direction of the vector when measured with respect to the +x axis and counter-clockwise as the positive direction. The possible answers are all negative angles, but the correct answer is not explicitly given.
  • #1
debabo007
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hi everyone, i was doing my physics homework and i had problems in these 2 MC quesitons.

#1 A vector originally at a direction of 30°, when measured counter-clockwise with respect to the +x axis, is rotated a further 30° counter-clockwise.
The magnitude of the vector will ...

a.Increase by a factor of four
b.Increase by a factor of two
c.Remain the same
d.Decrease by a factor of two
e.Decrease by a factor of four

#2 The components of vector are Ex = +150 N/C and Ey = -100 N/C.
If we measure all angles with respect to the +x axis and counter-clockwise as the positive direction, the direction of is closest to:


a. -326°
b. -56°
c. -34°
d. +34°
e. +304°
 
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  • #2
1) What do you think?

2) Draw the components.
 
  • #3
1) draw a 30 degree, and 60 degree angle. but think about this: does your magnitude have anything to do with the changing of angles?
 

FAQ: What Happens to the Magnitude of a Vector When Rotated?

What is a vector?

A vector is a quantity that has both magnitude and direction. It is often represented graphically as an arrow, with the length of the arrow representing the magnitude and the direction of the arrow representing the direction.

What are the different types of vectors?

There are two main types of vectors: displacement vectors and force vectors. Displacement vectors represent the change in position of an object, while force vectors represent the push or pull on an object.

How are vectors represented mathematically?

Vectors are typically represented using ordered pairs or column matrices. In two dimensions, a vector can be represented as (x,y) or [x,y]. In three dimensions, it can be represented as (x,y,z) or [x,y,z].

What is the difference between a scalar and a vector?

A scalar is a quantity that has only magnitude, while a vector has both magnitude and direction. For example, temperature is a scalar quantity, while displacement is a vector quantity.

How are vectors used in science and engineering?

Vectors are used in various fields of science and engineering, including physics, engineering, and computer science. They are useful for representing physical quantities, such as velocity and acceleration, and for solving problems involving forces and motion.

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