Mutiply Vectors: Find ?i + ?j + ?k

[queenspublic]

Homework Statement

Two vectors, r and s, lie in the xy plane. Their magnitudes are 4.50 and 7.45 units, respectively, and their directions are 320° and 85°, respectively, as measured counterclockwise from the positive x axis. What is the value of r x s ?

Express answer in this form: ?i + ?j + ?k

Homework Equations

(4.50 x 7.45)(sin235) <<< That should be the answer, is it?

The Attempt at a Solution

 

[berkeman]

Homework Statement

Two vectors, r and s, lie in the xy plane. Their magnitudes are 4.50 and 7.45 units, respectively, and their directions are 320° and 85°, respectively, as measured counterclockwise from the positive x axis. What is the value of r x s ?

Express answer in this form: ?i + ?j + ?k

Homework Equations

(4.50 x 7.45)(sin235) <<< That should be the answer, is it?

The Attempt at a Solution

Almost. First, the "x" there is the cross product, not multiplication. Second, the result of taking the cross product of two vectors is a scalar or a vector?

 

[LowlyPion]

What they are asking for is the cross product of the two vectors.

http://en.wikipedia.org/wiki/Cross_product#Definition

The resultant will be in the direction normal to the x,y plane. You must choose the direction by the right hand rule illustrated at the link.

 

[queenspublic]

It produces a scalar, doesn't it?

 

[berkeman]

It produces a scalar, doesn't it?

Nope. Here's a link from LowlyPion that should help:

http://en.wikipedia.org/wiki/Cross_product#Definition

.

 

[queenspublic]

Okay, so didn't I do it correctly with the 4.5 times 7.45 times sin of 235?

If yes, how do I convert into the dot product form: ?i + ?j + ?k ?

I'm confused. Can you please just show me how to get the answer?

 

[berkeman]

Okay, so didn't I do it correctly with the 4.5 times 7.45 times sin of 235?

If yes, how do I convert into the dot product form: ?i + ?j + ?k ?

I'm confused. Can you please just show me how to get the answer?

I undeleted LowlyPion's post above, because it contains extra hints that may help you. And no, we cannot show you how to get the answer, beyond offering hints and clearing up confusions, like the following...

Xi + Yj + Zk is NOT the "dot product form" of anything. It is the rectangular representation of a vector. In the original post, you were asking about doing a cross product, which is different from a dot product. You should review what your textbook says about each, and how to calculate it. You can also review the wikipedia pages on the operations.

 

[queenspublic]

The wikipedia page is just as confusing as my textbook. But both mentioned that formula which I used.

(4.50 x 7.45)(sin235) = -27.5

 

[queenspublic]

It's zero for the first two unit vector notations. I'm still confused.

 

[LowlyPion]

If the components of the vectors A and B both lie in the x,y plane where will the Resultant Cross Product be pointing?

Did you review the info on Wikipedia on the right hand rule?

Note there is slightly more info at:
https://www.physicsforums.com/library.php?do=view_item&itemid=85

But I think the Wikipedia entry should serve your purposes at visualizing what's happening.

 

[queenspublic]

27...that's the last notation. thanks everybody.