Why is the cross product only in 3 and 7 dimensions?

The cross product only exists in three and seven dimensions as one can always define a multiplication on a space of one higher dimension as above, and this space can be shown to be a normed division algebra.

Can a vector have more than 3 dimensions?

It is correct that one needs only three dimensions to specify, for example, the center of the object. However, even if the center of a rigid object is specified, the object could also rotate. In fact, it can rotate in three different directions, such as the roll, pitch, and yaw of an airplane.

What is the maximum value of cross product of two vectors?

Therefore, the maximum value for the cross product occurs when the two vectors are perpendicular to one another, but when the two vectors are parallel to one another the magnitude of the cross product is equal to zero.

Can a vector have multiple dimensions?

A vector is a mathematical quantity that has a magnitude and a direction. Vectors can be either two dimensional, with components in the x and y directions, or three dimensional, with components in the x, y, and z directions.

Can a vector have more than 2 components?

Any vector directed in two dimensions can be thought of as having two different components.

When cross product is maximum?

Under what condition is the cross product of two given vectors I Max II minimum?

The Brainliest Answer! R is maximum when Cos ( A, B) = +1 ie angle between vectors A and B is zero ie vectors A and B are parallel to each other. The resultant of two vector is minimum when both vectors are equal and in opposite direction i.e. the angle between the vector is 180 degrees.

Can you cross product 2d vectors?

Yes. Technically any two vectors that are not parallel to one another constitute a 2-D plane. The cross product then falls into a third dimension that is perpendicular to both of these vectors. However, you cannot cross product two 2-D vectors and have the resulting cross product also appear in the same 2-D space.