Which to use->Dot or cross product

Thread starter Celestiela
Start date May 28, 2005
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Cross Cross product Product

In summary, the dot product is a mathematical operation that takes two vectors and returns a scalar quantity, while the cross product returns a vector perpendicular to the original vectors. The dot product is used to calculate work, angles, and projections, while the cross product is used for torque, momentum, and area/volume calculations. The dot product is commutative and distributive, while the cross product is anti-commutative and distributive. They are both related to the angle between vectors. The dot product is calculated by multiplying corresponding components and adding them, while the cross product is calculated using a 3x3 matrix determinant.

May 28, 2005

Celestiela

a crate is sliding (disregard friction) with d=(-3.0 m)i while a steady wind pushes against the crate F=(2.0 N)i + (-6.0 N)j

How much work is done by the wind on the crate?

Ok W=Fd so I want to multiply the two vectors together.

[(-3.0 N)i ]*[(2.0 N)i + (-6.0 N)j ]

Do I use a cross product or a dot product? Why?

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May 28, 2005

whozum

The answer is in the proper defining equation of work.

May 28, 2005

Celestiela

D'OH

Working on homework on the weekends again...

:zzz:

Thanks!

FAQ: Which to use->Dot or cross product

What is the difference between dot and cross product?

The dot product, also known as the scalar product, is a mathematical operation that takes two vectors and returns a scalar quantity. It is calculated by multiplying the magnitudes of the two vectors and the cosine of the angle between them. The result of the dot product is a single number rather than a vector. On the other hand, the cross product, also known as the vector product, is a mathematical operation that takes two vectors and returns a vector perpendicular to both of the original vectors. It is calculated by multiplying the magnitudes of the two vectors and the sine of the angle between them. The result of the cross product is a vector rather than a scalar.

When should I use the dot product?

The dot product is often used in physics and engineering to calculate the work done by a force, the angle between two vectors, or the projection of one vector onto another. It is also used in geometry to determine if two vectors are perpendicular or parallel.

When should I use the cross product?

The cross product is commonly used in physics and engineering to calculate torque, angular momentum, or magnetic fields. It is also used in geometry to find the area of a parallelogram or the volume of a parallelepiped.

What are the properties of dot and cross product?

The dot product is commutative, meaning that a·b = b·a, and distributive, meaning that a·(b + c) = a·b + a·c. It is also related to the angle between the two vectors, as the dot product of two perpendicular vectors is 0, and the dot product of two parallel vectors is the product of their magnitudes. The cross product is anti-commutative, meaning that a×b = -b×a, and distributive, meaning that a×(b + c) = a×b + a×c. It is also related to the angle between the two vectors, as the cross product of two parallel vectors is 0, and the cross product of two perpendicular vectors is the product of their magnitudes.

How do I calculate the dot and cross product?

The dot product is calculated by multiplying the corresponding components of the two vectors and adding them together. For example, if vector a = (a1, a2, a3) and vector b = (b1, b2, b3), then the dot product a·b = a1b1 + a2b2 + a3b3. The cross product is calculated by using the determinant of a 3x3 matrix. For example, if vector a = (a1, a2, a3) and vector b = (b1, b2, b3), then the cross product a×b = (a2b3 - a3b2, a3b1 - a1b3, a1b2 - a2b1).