Finding the Dot Product of Vector A & B

In summary, the problem is asking for the scalar product of two vectors, A and B, with magnitudes of 5.00 units and 9.00 units respectively and an angle of 49° between them. To solve this, we use the formula A.B = (magnitude A)(magnitude B)cos \theta, where \theta is the angle between A and B. By plugging in the given values, we get A.B = (5N)(9N)cos 49°. The final answer is the magnitude of this product, which can be calculated using the Pythagorean theorem.
  • #1
chocolatelover
239
0

Homework Statement


Vector A has a magnitude of 5.00 units, and vector B has a magnitude of 9.00 units. The two vectors make an angle of 49° with each other. Find (vector A)(vector B)


Homework Equations





The Attempt at a Solution



(5i+0j)(0i+9j)=
(5N)(0m)+(0N)(9m)=

square root (5^2+0^2)
=5N

Could someone please tell me if this is correct and if not could someone show me how to do it?

Thank you very much
 
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  • #2
chocolatelover said:
Find (vector A)(vector B)

(vector A)(vector B)?

This notation does not mean anything. Possibly, you mean the scalar product A.B?

How did you utilize the 49 deg given in the problem?

A.B = (magnitude A)(magnitude B)cos [itex]\theta[/itex], where [itex]\theta[/itex] is the angle between A and B.

Take my advice given in the other post.
 
  • #3
Thank you

Regards
 

FAQ: Finding the Dot Product of Vector A & B

1. What is the dot product of two vectors?

The dot product of two vectors is a mathematical operation that results in a scalar quantity. It is also known as the scalar product or inner product. It is calculated by multiplying the corresponding components of the two vectors and adding them together.

2. How do you calculate the dot product of two vectors?

To calculate the dot product of two vectors, you first multiply the corresponding components of the vectors. For example, if vector A is (a1, a2, a3) and vector B is (b1, b2, b3), the dot product is calculated as (a1*b1 + a2*b2 + a3*b3). Then, you add all the products together to get the final scalar value.

3. What is the geometric interpretation of the dot product?

The dot product of two vectors has a geometric interpretation as well. It represents the magnitude of one vector projected onto the other vector, multiplied by the length of the other vector. This can also be thought of as the amount of one vector in the direction of the other vector.

4. What are some applications of the dot product in science and engineering?

The dot product has various applications in science and engineering. It is used in physics to calculate work and energy, in electric circuits to calculate power, in computer graphics and 3D modeling to calculate lighting effects, and in machine learning to calculate similarity between data points, among others.

5. Can the dot product of two vectors be negative?

Yes, the dot product of two vectors can be negative. This happens when the angle between the two vectors is greater than 90 degrees. In this case, the projection of one vector onto the other is in the opposite direction, resulting in a negative value for the dot product.

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