- #1
0517
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what can be defined by the following equation?
im new to calculus, and I'm totally lost now :(
im new to calculus, and I'm totally lost now :(
What is the Equation for the Scalar and Vector Products of Two Vectors?
In summary, the conversation discusses an equation that defines the angle between two vectors and how to calculate its value. The equation is a · b = |a| |b| cos θ, and its square is |a|2 |b|2 cos2θ.
- #2
tiny-tim
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welcome to pf!
hi janice! welcome to pf!
(try using | on your keyboard and the X2 icon just above the Reply box)
hint: if the angle between vectors a and b is θ, what does the equation say?
hi janice! welcome to pf!
(try using | on your keyboard and the X2 icon just above the Reply box
)hint: if the angle between vectors a and b is θ, what does the equation say?
- #3
I like Serena
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0517 said:what can be defined by the following equation?
im new to calculus, and I'm totally lost now :(
I guess you need to know that:
1. (a, b) = |a| |b| cos phi
2. |a x b| = |a| |b| sin phi
- #4
0517
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tiny-tim said:hi janice! welcome to pf!
(try using | on your keyboard and the X2 icon just above the Reply box
hint: if the angle between vectors a and b is θ, what does the equation say?
urgh, good question.
i didn't know how to answer, i think I'm super blur in this topic :(
- #5
0517
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tiny-tim said:hi janice! welcome to pf!
(try using | on your keyboard and the X2 icon just above the Reply box
hint: if the angle between vectors a and b is θ, what does the equation say?
0517 said:
a · b = |a| |b| cos θ
so the square of it = ? @@
- #6
tiny-tim
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0517 said:
|a|2 |b|2 cos2θ
and the square of the second part is … ?
1. What is the difference between scalar and vector products?
The main difference between scalar and vector products is the type of mathematical operation that is used. Scalar products involve multiplying two scalars (numbers) together, resulting in a scalar quantity. Vector products, on the other hand, involve multiplying two vectors together, resulting in a vector quantity.
2. How are scalar and vector products used in physics?
Scalar products are often used to calculate various physical quantities, such as work and energy. Vector products are used to calculate quantities related to rotational motion, such as torque and angular momentum. They are also important in understanding the direction and magnitude of forces in physics.
3. Can scalar and vector products be negative?
Yes, both scalar and vector products can be negative. The sign of the product depends on the angle between the two vectors being multiplied. If the angle is greater than 90 degrees, the product will be negative. Additionally, the direction of the resulting vector in a vector product can also be negative depending on the direction of the vectors being multiplied.
4. How do you calculate the magnitude of a vector product?
The magnitude of a vector product, also known as the cross product, can be calculated using the formula: |A x B| = |A||B|sinθ, where A and B are the two vectors being multiplied and θ is the angle between them. This formula can also be used to determine the direction of the resulting vector.
5. Is the scalar product commutative?
No, the scalar product is not commutative, meaning the order of the vectors being multiplied matters. In other words, A ∙ B does not necessarily equal B ∙ A. However, the vector product is anti-commutative, meaning A x B = -B x A. This is due to the fact that the scalar product only considers the magnitudes of the vectors, while the vector product also takes into account the direction of the vectors.
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