Vector Cross Product: Perpendicular Vectors lV_1 x V_2l

In summary, the magnitude of the cross product between two perpendicular vectors V_1 and V_2 is equal to the product of the magnitudes of the vectors and the cosine of the angle between them. This only applies in 3 dimensional space and there is a sign ambiguity. There was a mistake in the original calculation, as the correct formula is |V_1| * |V_2| * sin(a).
  • #1
horsegirl09
16
0
If vectors V_1 and V_2 are perpendicular, lV_1 x V_2l =? I know that if they are parallel for vector cross product, they equal 0.
 
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  • #2
horsegirl09 said:
If vectors V_1 and V_2 are perpendicular, lV_1 x V_2l =? I know that if they are parallel for vector cross product, they equal 0.
The cross product is a vector perpendicular to V_1 and V_2. Also V_1 and V_2 don't have to be perpendicular to each other, only not parallel.

Note that this only makes sense in 3 dimensional space.

Further note: the magnitude is |V_1|x|V_2|cos(a), where a is the angle between the vectors. There is a sign ambiguity.
 
Last edited:
  • #3
Isn't it |V_1|*|V_2|*sin(a)?
 
  • #4
ehj said:
Isn't it |V_1|*|V_2|*sin(a)?

You're right - my bad.
 

What is the definition of a vector cross product?

A vector cross product is a mathematical operation that takes two vectors and calculates a new vector that is perpendicular to the original two vectors.

How is the magnitude of a vector cross product calculated?

The magnitude of a vector cross product can be calculated by taking the product of the magnitudes of the two original vectors and the sine of the angle between them.

What is the geometric interpretation of a vector cross product?

The geometric interpretation of a vector cross product is the area of a parallelogram formed by the two original vectors.

How does the direction of a vector cross product relate to the original vectors?

The direction of a vector cross product is determined by the right-hand rule, where the direction is perpendicular to the plane formed by the two original vectors.

What are some practical applications of vector cross products in science?

Vector cross products are commonly used in physics and engineering to calculate forces, torque, and electromagnetic fields. They are also used in 3D graphics and computer vision algorithms for calculating orientation and movement in 3D space.

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