Square a Vector: Magnitude x Vector

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In summary, the dot product is a generalization of multiplication to vectors, and it can be used to find the squared norm of a vector. However, you cannot directly "square" a vector because there is no distinct "multiply" operation defined for vectors. Additionally, when trying to find the squared norm of a vector, be sure to include all necessary factors in your calculation to avoid incorrect results.
  • #1
MrLobster
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How do you sqaure a vector?

Is it the magnitude of the vector times the vector?
 
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  • #2
You can't "square" a vector, because there's no distinct "multiply" operation defined for vectors.

The dot product is a generalization of multiplication to vectors, and you can certain take the dot product of a vector with itself. The resulting quantity is the squared norm of the vector.

- Warren
 
  • #3
chroot said:
You can't "square" a vector, because there's no distinct "multiply" operation defined for vectors.

The dot product is a generalization of multiplication to vectors, and you can certain take the dot product of a vector with itself. The resulting quantity is the squared norm of the vector.

- Warren

would this mean just the square of each term added together?

ive tried this but then end upwith an answer different to the one given, i have a factor of sin($) missing.
 
  • #4
UniPhysics90 said:
would this mean just the square of each term added together?

ive tried this but then end upwith an answer different to the one given, i have a factor of sin($) missing.

Maybe if you state the question, and your attempts at the question, then it may be possible to answer you.
 
  • #5


Squaring a vector means multiplying it by itself. So, yes, it would be the magnitude of the vector multiplied by the vector itself. This can be represented mathematically as v², where v is the vector. Another way to think about it is finding the dot product of the vector with itself, which would result in the squared magnitude of the vector.
 

1. What does it mean to square a vector?

Squaring a vector involves multiplying each component of the vector by itself. For example, if we have a vector (2,3), squaring it would result in (4,9).

2. How do you calculate the magnitude of a vector?

The magnitude of a vector is calculated by taking the square root of the sum of the squares of each component. In other words, using the Pythagorean theorem: magnitude = √(x²+y²+z²).

3. Why is it important to square the magnitude of a vector?

Squaring the magnitude of a vector allows us to find the total length or size of the vector. It is also essential in many mathematical and scientific calculations, such as finding the distance between two points or determining the force of a vector.

4. What is the difference between the magnitude and the squared magnitude of a vector?

The magnitude of a vector is the actual length or size of the vector, while the squared magnitude is the magnitude multiplied by itself. Squaring the magnitude is useful in some calculations because it eliminates the use of square roots, making the calculations simpler.

5. Can you square a vector with negative components?

Yes, you can square a vector with negative components. The result will be a positive vector with the same direction and magnitude as the original vector. For example, if we have a vector (-2,3), squaring it would result in (4,9).

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