A vector is a mathematical entity that represents both magnitude and direction. It is typically represented by an arrow pointing in the direction of the vector with its length representing the magnitude.
To find vector b, you can use the formula b = a x c, where c is a unit vector perpendicular to a. In this case, c would be the vector (0,0,1). This will give you a vector b that is perpendicular to a and has a magnitude of 3.
Yes, a vector can be perpendicular to another vector with any magnitude. Perpendicularity only depends on the direction of the vectors, not their magnitudes.
No, a vector cannot be perpendicular to itself. A vector is always perpendicular to another vector, not to itself.
Finding a vector perpendicular to another vector is important in many applications, such as calculating forces in physics or finding the shortest distance between two lines in geometry. It also helps in understanding the relationship between two vectors in a given space.