How Does Doting a Unit Vector With a Vector A Affect the Result?

In summary: So, in summary, the correct answer is e, as the unit vector multiplied by the vector A will give the magnitude of A in the direction of the unit vector, but the sign may be negative if the angle between the two vectors is greater than 90 degrees.
  • #1
Tiven white
58
0

Homework Statement


When a vector A is dotted with a unit vector, the result is...
Select one:
a. zero
b. the magnitude of the unit vector in the direction of A.
c. the magnitude of A.
d. the angle between A and the unit vector.
e. the magnitude of A in the direction of the unit vector.


Homework Equations





The Attempt at a Solution


i said the answer is e reason being the unit vector is a form of direction and when multiplied by a vector it will give the magnitude of A in the corresponding direction.
is this correct?
 
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  • #2
Yes, that's the answer they're looking for, but the question is not worded very well. Magnitude implies that the result is positive, and ##\vec{A}\cdot \hat{u}## could very well be negative if the angle between the two vectors is greater than 90 degrees. ##\vec{A}\cdot\hat{u}## is the scalar projection of ##\vec{A}## in the direction of ##\hat{u}##.
 
  • #3
Tiven white said:

Homework Statement


When a vector A is dotted with a unit vector, the result is...
Select one:
a. zero
b. the magnitude of the unit vector in the direction of A.
c. the magnitude of A.
d. the angle between A and the unit vector.
e. the magnitude of A in the direction of the unit vector.


Homework Equations





The Attempt at a Solution


i said the answer is e reason being the unit vector is a form of direction and when multiplied by a vector it will give the magnitude of A in the corresponding direction.
is this correct?
Yes. I would call it the "component" of A in the direction of the unit vector.
 
  • #4
I agree, the wording is poor. In British English, I would interpret b and e as

b. (the magnitude of the unit vector), (in the direction of A.)
e. (the magnitude of A), (in the direction of the unit vector.)

which makes correct answer "none of the above".

If you interpret it as
b. (the magnitude) of (the unit vector in the direction of A.)
e. (the magnitude) of (A in the direction of the unit vector.)

which makes sense in British English for b, but not for e, the answer would be e.
 
  • #5
I don't have any problem interpreting the above question. I think the answer #4 above unnecessarily complicates things by inserting groupings that make no sense. Vela makes a good point about the sign however.
 

What is a unit vector times a vector?

A unit vector times a vector is a mathematical operation that involves multiplying a vector by a unit vector, which has a magnitude of 1 and points in the same direction as the original vector. This operation is used to find the component of the vector in the direction of the unit vector.

How do you calculate the result of a unit vector times a vector?

The result of a unit vector times a vector can be calculated by taking the dot product of the two vectors. This involves multiplying the magnitudes of the two vectors and the cosine of the angle between them.

What is the significance of a unit vector times a vector?

The result of a unit vector times a vector represents the component of the original vector in the direction of the unit vector. This can be useful in solving problems involving forces, motion, and other physical phenomena.

What are some properties of a unit vector times a vector?

One property of a unit vector times a vector is that the result is always a scalar quantity, meaning it has only magnitude and no direction. Additionally, the result will be positive if the two vectors are in the same direction, negative if they are in opposite directions, and zero if they are perpendicular to each other.

Can a unit vector times a vector be greater than the original vector?

No, the result of a unit vector times a vector will always be less than or equal to the magnitude of the original vector. This is because the unit vector essentially acts as a scaling factor for the original vector in the direction of the unit vector, but cannot increase its magnitude.

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