Statics: Dimensionless Unit Vector

[belvol16]

Homework Statement

Homework Equations

The Attempt at a Solution

So I began by subtracting.
(205-160)=55 i
(495+128)=623 j
Both of these vectors are in the positive direction. So if I divide the vector by its magnitude I should get an answer of 1 in the positive direction for both i and j.
The online book lists the answers as R hat = 0.0720 i + 0.997 j . I guess I'm not sure how the book got these answers. I thought unit vectors always had a magnitude of 1 and their purpose was to determine the direction of the vector.
Thank You!

 

[Doc Al]

So if I divide the vector by its magnitude I should get an answer of 1 in the positive direction for both i and j.

If each component had a magnitude of 1 then the vector would not be a unit vector!

The online book lists the answers as R hat = 0.0720 i + 0.997 j . I guess I'm not sure how the book got these answers. I thought unit vectors always had a magnitude of 1 and their purpose was to determine the direction of the vector.

The unit vector does have a magnitude of 1. Given those components, find the magnitude of the full vector. What do you get?

 

[Mark44]

Minor point, but $\vec{B} - \vec{A}$ has units of lbs, and so would a unit vector in this direction. I'm puzzled by the instruction to "find a dimensionless unit vector" in this direction.

 

[Doc Al]

Minor point, but $\vec{B} - \vec{A}$ has units of lbs, and so would a unit vector in this direction. I'm puzzled by the instruction to "find a dimensionless unit vector" in this direction.

If you divide by the magnitude (also in lbs) you can get a dimensionless direction vector.

 

[Mark44]

If you divide by the magnitude (also in lbs) you can get a dimensionless direction vector.

OK, that makes sense. Objection withdrawn...