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

• queenspublic
In summary, the vectors A and B have a resultant vector that points in the direction of the cross product of their directions, or normal to the x,y plane.
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

Last edited:
queenspublic said:

## 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?

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.

It produces a scalar, doesn't it?

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?

queenspublic said:
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.

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

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

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?

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.

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

## 1. What is the purpose of multiplying vectors?

Multiplying vectors allows you to find the scalar or vector quantity that results from combining two or more vectors.

## 2. How do you perform vector multiplication?

There are two types of vector multiplication: dot product and cross product. The dot product involves multiplying corresponding components of two vectors and then adding the results, while the cross product involves using a specific formula to calculate a new vector that is perpendicular to the two original vectors.

## 3. What is the result of multiplying two vectors?

The result of multiplying two vectors can be a scalar quantity or a vector quantity, depending on the type of vector multiplication used. The dot product results in a scalar, while the cross product results in a vector.

## 4. How do you find the components of the resulting vector?

For the dot product, the components of the resulting scalar can be found by multiplying the corresponding components of the two original vectors and then adding them together. For the cross product, the components of the resulting vector can be calculated using a specific formula that involves the two original vectors.

## 5. What are some real-world applications of vector multiplication?

Vector multiplication is used in many scientific and engineering fields, such as physics, mechanics, and computer graphics. It can be used to calculate work and torque, determine the direction of magnetic fields, and create 3D models and animations.

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