# Multiplying a Vector Product by Another Vector

• student34
In summary: Sorry for the confusion. In summary, the conversation discusses a question asking to calculate (AxB)·C, where A and B are both in the xy-plane with given magnitudes and directions, and C is in the +z-direction with a given magnitude. The conversation also mentions the equations (A×B) = ABsinθ = D and D·C = DCcosσ = R, which are used to solve the problem. The participants discuss the use of the dot in the equation and whether it implies a scalar or vector product. They also mention the use of the right-hand rule to determine the direction of the product. Ultimately, they come to the conclusion that the answer should use cos instead of sin and discuss the reasoning
student34

## Homework Statement

The question asks to calculate (AxBC, where A's magnitude is 5.00, B's magnitude is 4.00, and they are both in the xy-plane. B is 37° counter clockwise from A. C has a magnitude of 6.00 and is in the +z-direction.

## Homework Equations

(A×B) = ABsinθ = D; D·C = DCcosσ = R

## The Attempt at a Solution

(A×B) = 5×4×sin37° = 12.363 = D. D·C = 12.363×6.00×sin90° = 72.2 = R which is the correct answer. But doesn't the dot in (A×BC imply a scalar product in which case the last part should be 12.363×6.00×cos90°?

Does the cross product yield a vector or a scalar?

student34 said:

## Homework Statement

The question asks to calculate (AxBC, where A's magnitude is 5.00, B's magnitude is 4.00, and they are both in the xy-plane. B is 37° counter clockwise from A. C has a magnitude of 6.00 and is in the +z-direction.

## Homework Equations

(A×B) = ABsinθ = D; D·C = DCcosσ = R

## The Attempt at a Solution

(A×B) = 5×4×sin37° = 12.363 = D. D·C = 12.363×6.00×sin90° = 72.2 = R which is the correct answer. But doesn't the dot in (A×BC imply a scalar product in which case the last part should be 12.363×6.00×cos90°?
You mean to say that $\vec{A} \times \vec{B} = (5)(4)(sin37°) \widehat{n}$, where n-hat is the unit vector orthogonal to both vectors.

Mandelbroth said:
You mean to say that $\vec{A} \times \vec{B} = (5)(4)(sin37°) \widehat{n}$, where n-hat is the unit vector orthogonal to both vectors.
... and don't forget to use the right-hand rule to get the direction of the product in relation to the z axis sign.

gneill said:
Does the cross product yield a vector or a scalar?

I don't know. It just asks to calculate (A×BC with the values that I gave above.

Mandelbroth said:
You mean to say that $\vec{A} \times \vec{B} = (5)(4)(sin37°) \widehat{n}$, where n-hat is the unit vector orthogonal to both vectors.

We haven't seen that n yet, so I don't think we are suppose to use it in this question.

student34 said:
We haven't seen that n yet, so I don't think we are suppose to use it in this question.

Mandelbroth just means n to be the direction that AxB points. You have to know that to find the angle between AxB and C. How is the direction AxB points related to the directions A and B point?

Dick said:
Mandelbroth just means n to be the direction that AxB points. You have to know that to find the angle between AxB and C. How is the direction AxB points related to the directions A and B point?

It would be in the positive direction, but isn't A×B perpindicular to C either way? And why does the answer seem to use sin90° instead of cos90°; doesn't the function (·) mean a scalar product?

student34 said:
It would be in the positive direction, but isn't A×B perpindicular to C either way? And why does the answer seem to use sin90° instead of cos90°; doesn't the function (·) mean a scalar product?

What do you mean by positive direction? Which positive? C points in the positive z direction. Which positive direction does AxB point? I don't think they are perpendicular. If the answer says sin(90), it really shouldn't. That's misleading. The answer should contain a cos. cos of what?

student34 said:
It would be in the positive direction, but isn't A×B perpindicular to C either way?
By definition, AxB is perpendicular to both A and B. What does that tell you about its direction in relation to C?

Dick said:
What do you mean by positive direction? Which positive? C points in the positive z direction. Which positive direction does AxB point? I don't think they are perpendicular. If the answer says sin(90), it really shouldn't. That's misleading. The answer should contain a cos. cos of what?

Ah, I got it now. Oh ya, and the answer did not have sin90°, I just fudged that in there to try to make sense of it all, but I realize now that it is cos0° - thanks.

haruspex said:
By definition, AxB is perpendicular to both A and B. What does that tell you about its direction in relation to C?

Thanks, I go it now.

student34 said:
Ah, I got it now. Oh ya, and the answer did not have sin90°, I just fudged that in there to try to make sense of it all, but I realize now that it is cos0° - thanks.
OK, but just to check... why cos(0) and not cos(180 degrees)?

[Deleted]

Last edited:
@Puky The question haruspex asked was directed towards the OP to check his understanding.

My mistake, I thought it was the OP who asked that question.

## What is a vector product?

A vector product, also known as a cross product, is a mathematical operation that combines two vectors to create a new vector that is perpendicular to both of the original vectors.

## How do you multiply a vector product by another vector?

To multiply a vector product by another vector, you can use the formula: (A x B) x C. This means that you first calculate the vector product of A and B, and then take the result and calculate the vector product with C.

## What is the purpose of multiplying a vector product by another vector?

The purpose of multiplying a vector product by another vector is to find the perpendicular component of the original vector with respect to the plane defined by the two other vectors. It is commonly used in physics, engineering, and mathematics to solve problems involving forces, motion, and rotation.

## Can you multiply a vector product by a scalar?

No, a vector product can only be multiplied by another vector. However, you can multiply a scalar by a vector product, which will result in a scaled version of the original vector product.

## What are some real-world applications of multiplying a vector product by another vector?

Multiplying a vector product by another vector is commonly used in applications such as calculating torque, finding the direction of magnetic fields, and determining the angular momentum of rotating objects. It is also used in computer graphics to create 3D effects and in geology to analyze the movement of tectonic plates.

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