Question

Can you cross product $ 4d $ vectors?

Answer 1

Hint: Here we are asked whether the four-Dimensional vector can undergo cross product or not, for that we will follow the basic concepts and then justify the resultant required answer.

Complete step by step solution:
A vector can be defined as the quantity which has both the magnitude and the direction and are represented by the directed line segment whose length represents the magnitude and the orientation represents the direction.
Cross product can be defined as the binary operation where the cross product gives the resultant vector. For the given two linearly independent vectors a and b, the cross product $ a \times b $ is the vector which is perpendicular to both a and b.
Cross product can be expressed as the determinants of order three and hence, it follows the right hand thumb rule so cross product can only work for three dimensional vectors and hence we can not find the cross product for four dimensions.

Note: Know the difference between the dot product and cross product and apply the concepts accordingly. Dot product follows the cumulative law whereas the cross product does not follow the cumulative law. Always remember that the cross product follows the right hand thumb rule whereas the dot product does not follow it. The result of the cross product is always the vector quantity.