Dot product between Spherical and Rectangular.

In summary, the dot product between Spherical and Rectangular coordinates is a mathematical operation that calculates the scalar product of two vectors in these coordinate systems. It is calculated by taking the product of the magnitudes of the two vectors and the cosine of the angle between them. This operation is significant as it allows for the conversion of vectors between these two coordinate systems and can also be used to find the angle between two vectors. The dot product is closely related to the cross product, as both operations are used to find the angle between vectors.
  • #1
Oscargot
1
0
Hello, I just have a question about dot products of different coordinate systems.
I was wondering if anyone can explain why unit vector z(rect.) DOT unit vector r(spherical) is equal to cos(theta). As well, I was hoping if anyone could explain z DOT (Theta) = -sin(theta)?
 
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  • #2
What is the definition of spherical coordinates?
 

FAQ: Dot product between Spherical and Rectangular.

What is the dot product between Spherical and Rectangular coordinates?

The dot product between Spherical and Rectangular coordinates is a mathematical operation that calculates the scalar product of two vectors in these coordinate systems. It is used to find the angle between two vectors and is an important concept in vector algebra and geometry.

How is the dot product calculated between Spherical and Rectangular coordinates?

The dot product between Spherical and Rectangular coordinates is calculated by taking the product of the magnitudes of the two vectors and the cosine of the angle between them. In other words, it is the sum of the products of the corresponding components of the two vectors.

What is the significance of the dot product between Spherical and Rectangular coordinates?

The dot product between Spherical and Rectangular coordinates is significant because it allows for the conversion of vectors between these two coordinate systems. This is useful in many applications, such as in physics and engineering, where different coordinate systems may be used for different purposes.

What is the relationship between the dot product and the angle between two vectors in Spherical and Rectangular coordinates?

The dot product between Spherical and Rectangular coordinates can be used to find the angle between two vectors in these coordinate systems. The dot product formula includes the cosine of the angle between the vectors, so by rearranging the formula, we can solve for the angle.

How does the dot product between Spherical and Rectangular coordinates relate to the cross product?

The dot product and the cross product are two different mathematical operations involving vectors. While the dot product results in a scalar value, the cross product results in a vector. However, both operations are used to find the angle between two vectors and are closely related in terms of their calculations.

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