Why is the cross product of two vectors the area?

Why is the cross product of two vectors the area?

Cross product of two vectors is the method of multiplication of two vectors. The cross product of two vectors is the third vector that is perpendicular to the two original vectors. Its magnitude is given by the area of the parallelogram between them and its direction can be determined by the right-hand thumb rule.

What does the magnitude of a cross product represent?

The cross product of two vector quantities is another vector whose magnitude varies as the angle between the two original vectors changes. The magnitude of the cross product represents the area of the parallelogram whose sides are defined by the two vectors, as shown in the figure below.

How do you find the magnitude of the cross product of two vectors?

The magnitude (or length) of the vector a×b, written as ∥a×b∥, is the area of the parallelogram spanned by a and b (i.e. the parallelogram whose adjacent sides are the vectors a and b, as shown in below figure). The direction of a×b is determined by the right-hand rule.

What is the magnitude of resultant of cross product of two parallel vectors A and B?

0
3. What is the magnitude of resultant of cross product of two parallel vectors a and b? Explanation: The resultant of cross product of 2 parallel vectors is always 0 as the angle between them is 0 or 180 degrees. So the answer is |a|.

What is the magnitude of the vector product between these two vectors?

The vector product of two vectors is a vector perpendicular to both of them. Its magnitude is obtained by multiplying their magnitudes by the sine of the angle between them. The direction of the vector product can be determined by the corkscrew right-hand rule.

Why is cross product called a vector product?

The other type, called the cross product, is a vector product since it yields another vector rather than a scalar. As with the dot product, the cross product of two vectors contains valuable information about the two vectors themselves.

What is the magnitude of the resultant of cross product of two parallel vector A and B?

What is the magnitude of the cross product of two parallel vectors the magnitude of the cross product of two parallel vectors is?

magnitude zero
The cross product is always orthogonal to both vectors, and has magnitude zero when the vectors are parallel and maximum magnitude ‖a‖‖b‖ when they are orthogonal.

How to find the magnitude of the cross product of two vectors?

Since when you multiply the magnitudes of two vectors and then multiply that product with the sinus of the angle between them you will get the magnitude of the cross product of those two vectors, you know that the magnitude of the cross product of two vectors is equal to the area of the parallelogram that those two vectors make

What is the cross product of a parallelogram?

The cross product is defined as the vector orthogonal to both vectors whose magnitude is , where is the angle between the two vectors. The direction is given by the right hand rule, but that is irrelevant for the purposes of this answer. The area of a parallelogram with sides and and an angle is .

What are the properties of cross-product?

The properties of cross-product are given below: Cross product of two vectors is equal to the product of their magnitude, which represents the area of a rectangle with sides X and Y. If two vectors are perpendicular to each other, then the cross product formula becomes:

What is the difference between cross product and dot product?

The cross product is mostly used to determine the vector, which is perpendicular to the plane surface spanned by two vectors, whereas the dot product is used to find the angle between two vectors or the length of the vector.