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

[Tiven white]

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?

 

[vela]

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 $\hat{u}$.

 

[Chestermiller]

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.

 

[AlephZero]

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.

 

[olivermsun]

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.